Hi! I don't know of any particular climate software like that... But the big thing to keep in mind about islands:
-Their temperature is often mitigated by being so surrounded by ocean. It's less extreme than inland weather at the same latitudes, in terms of temperatures.
Now, islands close to a big continent have similar climates to their coastal counterpart. E.g., the islands of the Puget Sound share nearly identical weather and climate with Seattle's surrounding area. What I'd personally do is just look up the weather of a real island similar in latitude to where you want your fictitious island to be, then copy it and tweak for things like changes in mountain ranges, etc.
Oh, and I think hand drawn maps are pretty popular here, so you don't have to worry about that!