In case of Sweden this would be possible as well on the West Coast as Sweden was even less prepared than Norway, which was at least trying to think what to do with the information. There's not even need for a large number of warships as it was the case with Norway as distance to Germany is shorter and there's no fear of RN and MN intervention. Thus civilian ships, more suitable for transporting troops and more inconspicious, can be used.
If we speculate on need for troops on traditional 2:1 superiority one would need six divisions. This would not cripple Fall Gelb in any way as there was some surplus of infantry divisions anyway. One motorized brigade (11. Schützen Brigade) was already deployed in Denmark and could be used as exploitation force.
Say, two divisions for Göteborg, one for Helsingborg, one for Malmö and one for Trelleborg and Scanian southern coast. Against these landings no precautions existed. Southern Sweden was not effectively mobilized yet.
When the Swedish field forces would be mobilized there's important difference between a division mobilized and a division which would be combat ready. Any units entering the battle with German units would be one haphazardily mobilized and not really combat ready.
As for Swedish equipment, a lot of it was still in Finland or being deployed in Northern Sweden. Severskys were not yet operational and the Swedish air force consisted of 122 operational military aircraft with beforementioned Gladiators forming the entire fighter force. Bomber force consisted of Hawker Harts with a few Ju-86's being only modern bombers.
Bf-110, most useful fighter in conquest of Norway, had ample combat range from German bases to be used in Southern Sweden. They could sweep the Gladiators, Harts and Ju-86's from the skies. Bases in Denmark would just help this.
Granted, Battle of Narvik would end up as German disaster but this would be rather small setback. The Allied position in Northern Norway was untenable in long term.
The difference is that the towns of western Sweden is behind an extensive archipelago, that is already partially mined. The Germans need pilots (or at least very accurate sea charts) and need to sail during daytime at low speeds to not run aground. It takes a day to navigate the archipelagos, and you'll pass forts, fishing villages, naval bases and simply small hamlets where anyone can raide the alarm. The coastal fortifications close to Göteborg are quite extensive (much better protected than the ones at Oslo, for example). The Germans can simply not steam right in during night like they did in the Norwegian fjords.
The Germans were already using their entire navy and almost every merchant ship that was available for the invasion of Norway - both for shipping in the troops and for supply. They landed two divisions in Norway and later transported in another three. They cannot land another two in Sweden at the same time. They simply do not have the capacity.
Any traditional attack demand 3:1 superiority. You have six Norwegian divisions and six Swedish (plus enough regular troops for another five divisions not organised into divisions), which means you need 32 German divisions for your 2:1 superiority and 48 for 3:1. How will the Germans supply all these troops oversea? Note that Denmark surrendered only after it was clear the Germans were not attacking Sweden. If Sweden is confirmed to be under attack, the Danish army will most likely see itself as honour-bound to at least put up token resistance and destroy airfields and infrastructure, which will mess up the German supply situation even more. The Danish navy would steam over to Sweden - and it had quite a number of coastal destroyers and submarines to add to the already extensive number of Swedish destroyers and submarines.
The main German problem however is not infantry, it is supplying an offensive over such distances. They will need to pull a lot of air units and transport planes out of the attack in the west to do this, and reduce the supply for Fall Gelb when fighting in Sweden and Norway. Note that it took the Germans 6 months to restore their stocks of ammunition and fuel after the Polish campaign.
The Bf 110C, of which 76 were commited to Weserübung, had an operational range of 770km. It does allow it to fly from Copenhagen to Stockholm, and operate for maybe ten minutes (the distance is 520km). The Swedish air force can easily base itself outside even the Bf 110 range.
It is a myth that Sweden gave away much of its equipment to Finland - most of what was given was returned in March and April. Sweden had 74 million rifle cartridges on hand and were producting more than 10 million a month in April 1940. By the end of the year, production was up to 20 million rifle cartridges a month.
12 J 9 Seversky were operational in 1:a/F8 on April 1940 and another 48 were in ship crates crossing the Atlantic. 12 J 11 CR.42 were available in depots. There were 56 B 3 (Ju 86), 43 B 4 (Hawker Hart), 47 S 6 (Fokker C.V). The first B 4 (Northrop A-17) was delivered in April 1940 and another 102 would be delivered before the end of the year. If Sweden and Norway continues to fight, the Hawk 75A, Seversky EP-35s and Vultee 48C Vengenaces will be delivered - through Narvik or Petsamo.
While the Germans might be able to sail into Helsingborg and Malmö harbours, and meet only token resistance, the squadron attacking Göteborg will have to sail through one of three possible sailing routes, that merge long before entering Göteborg harbour, all covered with forts (and we're talking multiple forts here, see the image below).
It is not possible to sail through this at nighttime, and the distance from the outer parts of the sailing channel to the harbour is at least 40km, probably more, that have to be sailed through at low speed.
Göteborgseskadern (under command of A.Cassel) in April 1940:
3. Pskdiv (HMS Manligheten, HMS Tapperheten) (Marstrand) - two armoured ships.
4. Jagardiv (HMS Ragnar, HMS Sigurd) (Marstrand) - two (old) destroyers
5. Jagardiv (HMS Wrangel, HMS Wachtmeister) (Kungsbacka) - two (old) destroyers.
3. Ubåtsdiv (HMUB Delfinen, HMUB Springaren, HMUB Nordkaparen) (Göteborg) - three submarines, small (4x533mm TTs, first delivered 1936)
6. Ubåtsdiv (HMUB Sälen, HMUB Hajen, HMUB Valrossen, HMUB Valen) (Varberg-Falkenberg) four submarines, same size, but from 1918.
3. Minsverpardiv (Styrbjörn, Starkodder, Hv 383, Hv 384) (Marstrand) four minesweepers.
1. Mtbdiv (T 3, T 4, T 11-T14) (Halmstad) six MTBs.
Hjkb 41 Skagerack - auxiliary gunboat.
Hjkb 43 Odin - auxiliary gunboat.
19. Vbdiv (6 Hv) - 6 patrolboats (usually 2nd ord 3rd class torpedo boats without TTs).
36. Vbdiv (6 Hv) - 6 patrolboats (usually 2nd ord 3rd class torpedo boats without TTs).
42. Vbdiv (6 Hv) - 6 patrolboats (usually 2nd ord 3rd class torpedo boats without TTs).
In addition, the following military units are stationed in Göteborg and the surrounding area;
Göteborgs Landstormsregemente (a regiment of local defence)
I6 infantry regiment.
I9 mixed regiment (one battalion infantry, one battalion tanks)
I15 infantry regiment
I16 infantry regiment
KA3 coastal artillery regiment (the coastal artillery had lots of 10,5cm bofors 1934 cannons that worked like field guns)
A2 artillery regiment
A9G AA battalion
But the bottom line is that the Germans committed their entire navy and as much of their merchant marine as they possibly could to Norway - and landed three divisions to later reinforce these troops with another three divisions. Note that all these troops were landed in proper harbours, unopposed. Where do they find the naval capacity to suddenly land and another four divisions, supply, support and reinforce them?