I've looked further into this.
These are the dates from Bismarck and Prinz Eugen leaving Gotenhafen to the Battle of the Denmark Strait IOTL and the dates if they left Gotenhafen 35 days earlier.
NB I know that it's unlikely that it would be exactly like that due to the longer days and different weather (for two things there will be others) but it's the best I can do and does give us a rough guide.
These are Hood's OTL movements between 6th and 21st April 1941 IOTL.
- 6th - At 0815 hours arrived at Scapa Flow escorted by destroyers ELECTRA, ESCAPADE, and TARTAR.
- (At 0900/6/4/41 the CinC HF in KING GEORGE V divided the area off Brest into 4 sectors A to D each 15º between bearings 213º and 273º, mean distance from Brest 560 miles.
- At 1535/6/4/41 the Admiralty signalled “Consider battlecruisers will probably leave Brest tonight”. This was because the GNEISENAU had moved out of dry dock into the inner harbour; which was in fact due to a 250lb UXB in the dock.)
- At 1946 hours sailed from Scapa Flow escorted by destroyers ZULU, MAORI and ARROW and sailed for position 50N, 20W in sector C off Brest.
- (At 0602/7/4/41 GNEISENAU was hit in the stern, and put out of action for 7 months, by a torpedo dropped by Bristol Beaufort OA-X of 22 Squadron RAF flown by F.O. Kenneth Campbell, who was posthumously awarded the VC. However, this was not known to the Admiralty for some time)
- 8th - At 0800 hours arrived at position 54N, 15-30W to commence patrol.
- 8th - At 1200 hours in position 50N, 21W RVed with cruiser KENYA.
- 10th - Destroyers ARROW and COSSACK detached to refuel at Londonderry.
- 11th - At 0800 hours the refuelled destroyers ARROW and COSSACK from Londonderry rejoined. Following which destroyers MAORI and ZULU detached to refuel at Londonderry
- 13th - The refuelled destroyers MAORI and ZULU from Londonderry rejoined.
- 15th - At 0630 hours arrived back at Scapa Flow escorted by destroyers COSSACK, ZULU, and MAORI. ARROW, who was unable to maintain the speed and had been detached, arrived at Scapa Flow later.
- 18th - At 1645 hours sailed from Scapa Flow in company with cruiser KENYA and destroyers COSSACK, MAORI and ZULU for the Biscay patrol to relieve KING GEORGE V.
- 19th - At 0120 hours following Admiralty order the HOOD force were diverted to Hvalfjord. (This deployment was to counter any attempt by the German battleship BISMARCK to break out into the Atlantic. Following a report of a German force passing through the Skagerrak)
- 21st - At 1000 hours arrived at Hvalfjord in company with COSSACK, INGLEFIELD, MAORI and ZULU.
These are King George V's movements between 13th and 22nd April 1941 IOTL.
- 13th - At 0107 hours KING GEORGE V, light cruiser NIGERIA, and destroyers MASHONA, ELECTRA and ESCAPADE departed Scapa Flow for position 46-30N, 18-10W to mount patrol off the Bay of Biscay. At 1800 hours position 57-48N, 9-35W.
- 14th - At 0515 hours unidentified aircraft sighted passing from port to starboard. At 0611 hours sighted a large group of unidentified aircraft passing from starboard to port. At 0618 sighted destroyers HMCS SAGUENAY and RESTIGOUCHE bearing 110¼. At 1039 hours radar reported single aircraft bearing 282¼, 14 miles. At 1130 hours position 54-44N, 12-39W.
- 15th - At 0800 hours position 50-30N, 19-14W, course 227¼, speed 19 knots. At 1045 hours destroyers MASHONA, ELECTRA and ESCAPADE were detached to refuel at Londonderry.
- 16th - At 0900 hours position 46-28N, 18-01W, course 220¼, speed 18 knots. At 0925 hours speed reduced to 17 knots due to heavy weather. At 1900 hours position 46-56N, 18-40W, and course 090¼.
- 17th - At 0800 hours position 44-05N, 17-07W and course 320¼.
- 18th - At 0800 hours position 44-37N, 17-48W, course 270¼, speed 18 knots.
- (Late on the 18/4/41 the Admiralty received a report that German battleship BISMARCK, two cruisers, cruiser Leipzig class and three destroyers passed the Skaw early morning of 18/4/41 steering north west. This report was false, as at the time the BISMARCK was in the Baltic)
- 19th - At 0001 hours position 45-31N, 17-21W and speed 21 knots. At 0150 hours altered course to 000¼ and increased speed to 20 knots to return to Scapa. At 0900 hours position 46-39N, 18-12W.
- 20th - At 0900 hours position 49-46N, 20-53W, course 060¼, speed 17 knots. KING GEORGE V and NIGERIA was joined by destroyers ESCAPADE, ELECTRA and MASHONA from Londonderry. At 1342 hours position 49-24N, 20-49W, course 043¼, speed 17½ knots.
- 21st - At 0350 hours received a report from CinC Western Approaches 0303/21; 'One Catalina aircraft missing. Following received at 0210/21 from Sunderland aircraft, begins: Distress flares seen in position 53-42N, 13-24W. No further news, searching, ends'. (This was Catalina AH 532 of 210 Squadron that was on an Atlantic Patrol from Loch Erne, N.I.) At 0628 hours altered course to 051¼ to search for missing Catalina. At 0900 hours altered course to 090¼. 0914 hours received Admiralty message 0909/21; 'Blue air raid message'. At 1213 hours KING GEORGE V opened fire with her 5.25in at aircraft identified as German.
- 22nd - At 0700 hours position 58-37N, 7-37W, course 085¼, speed 17½ knots. At 1552 hours KING GEORGE V, light cruiser NIGERIA and destroyers ESCAPADE, ELECTRA and MASHONA arrived at Scapa.
The source for both is Naval History Net.
I think it's quite likely that a Swedish warship would have sighted the German warships on 15th April, reasonable to expect a British reconnaissance aircraft to spot them in Grimstadfjord on 16th April and for Norfolk or Suffolk to spot them on 18th April. (I wrote in an earlier post that the two cruisers patrolled the Denmark Strait in April 1941 IOTL.)
Hood was at Scapa Flow on 15th April having arrived at 0630 the same day. My guess is that she'd be refuelled and ordered to sail for Hvalfjord PDQ. IOTL it took 2 days to sail from Scapa Flow to the Denmark Strait (22nd to 24th May 1941) so it looks like there's enough time for her to be in position on 19th April ITTL.
King George V was blockading The Twins in Brest on 18th April, she set course for Scapa Flow early the next day and was back at Scapa Flow on 22nd April, which was 4 days later. Those were her movements IOTL following the false alarm of 18th April 1941.
King George V was also blockading the Twins in Brest on 15th April. So it looks as if the ships were sighted by the Swedes on that day ITTL she could be at Scapa Flow on 19th April but there isn't time to get her to the Denmark Strait by that date.
I used this website to see what the positions in Naval History Net were on a map.
Find latitude and longitude by clicking a map, entering zip code/address. Batch geocode locations. Convert latitude-longitude, GPS coordinates, decimal degrees, degrees mins secs...
www.findlatitudeandlongitude.com
If my research and estimates are correct Hood would be fighting Bismarck and Prinz Eugen on 19th April 1941 without the support of King George V.