You keep saying that, "Once the Suez is closed after the Japanese attack", but where in this thread is that written? I don't see the Japanese going into this unless the Italians are already having to go the long way round Africa, as only that would make their supply ships vulnerable. So the proper sequence is, the UK closes the Suez, and if that doesn't do the trick, then the Japanese DoW Italy.
If you were not thinking along those lines, that would explain much. So;
1) UK closes Suez to Italian shipping sometime after the fighting starts. (If they close it before, then we get no war)
2) Italy continues their war (to be fair, they have little choice, and I myself would order the same thing).
3) Japan jumps into the fray. (And now we can have an unlikely, but very interesting little war)
Someone posted the Japanese conducting naval bombardments, but what about minefields? If you try to race in during the hours of darkness, conduct a bombardment like during the OTL Guadalcanal campaign, and then race away to be out of range of land based air attack, you are taking a huge risk with no hope of being able to clear the mines from your path.
Someone also posted the use of small landing parties conducting raids, but this begs the issue of how to pull them out again. A nighttime naval bombardment takes a short time, a nighttime landing, followed by movement to contact, conducting the attack, getting back to the extraction point, and only then being able to begin the withdrawl portion of the operation...
Infiltration of small teams, bearing gifts for the locals, that can get "boots on ground in country", and enabling setting up a network to smuggle supplies, arms and ammunition to the Ethopians would make sense, but you wouldn't want to mix commando raids with this effort.
I keep telling that because is the only way that made sense; if the British close Suez after the invasion (in totally contrast of their previous policy and showing a risk taking attitude previously unseen) is started there will be a serious diplomatic crisis between the two nation and Benny will go for other way to try to supply the military effort but as LordKalvan as said, things in the end will cool down and some negotiating way will be found...even if the risk of a shooting war will looming over all the process and the diplomatic situation will be a mess in the aftermath.
If the Japanese intervene the entire situation will precipitate immediately, and frankly it's very probable that the British will sunk the japanese ships themselfs for having transformed a complicated and tense situation in a clustefuck of epic proportion war what it seem no reason.
Conduction night raids and nightime bombardment it's not that easy...at least if you desire make it efficient; sending time bringing gifts pose a simple problem aka how this team will reach the Ethiopians? The coast and a lot (and i mean a lot) of hinterland are italian held, the territory itselfs it's not very forgiving and without locals helping they don't stand a change to survive long.
Plus you can't do that for very long unless you have some base for the ships and lot of supply.