For an advanced, prosperous and populous country; Japan has markedly little capability to project power away from its own territory.
That is what will likely change as a result of this. Abe has been pushing for legal and military capability to fight outside the country, and this will strongly support some change.
In the short term, they can fund another country to strike for them, or possibly hire mercenaries. It would also be an interesting exercise for their Intelligence services.
“Japan has markedly little capability to project power away from its own territory.”
Their navy is actually currently bigger than the British Royal Navy. Better qualitatively too. The Brits are a mere shadow of what they had in 82.
They also have a bigger air force than the UK, also with a qualitative advantage. Assuming Japanese F-15s to be the betters of Eurofighters.
Neither has any strategic bombers.
Basically, Japan can slightly out project the UK just about now if they choose.
A few plane-loads of munitions and weapons given to the Kurds would likely go a long way.