Start in the south and work north to get not hellishly hot weather in the south and avoid chilly in the north.

Southern Spain is much hotter than others and as soon as you reach the Alps (and north) it will be cooler and rainier.

Greek islands you need to save until the end - off season they are dead.

Oh - and it will rain - maybe a lot, maybe a little - but I have never been to europe for more than 2 or 3 days without rain (except southern Spain)

April in Germany and Switzerland will likely be cool and possibly wet. In fact we were in Wengen one july and the locals said the trails hadn't dried up till mid June that year.. so ... I would skip both those countries in April ,, you already have so many awesome choices. I do not beleive any of the those places ( including Spain etc) will be hot in april or may, they will just be nice.
I think people sometimes mistakenly think that the mediterraen countries are tropical weather wise, they are not, they get cool and rainy in winter ( heck places like Barcelona and Rome have even gotten freak snow ) and dont' warm up till late spring( late march thru April)

Well, it won't be "hellishly hot" anywhere in Europe in April to mid-May, so you can set aside that worry. I certainly wouldn't start my trip in the Greek Islands in April, because the season hasn't yet started, and most hotels and restaurants will still be closed. One of the major hiking attractions on the islands, Crete's Samaria Gorge, doesn't open until May. In early April there may even still be skiing in the Greek mountains: http://www.snowcam.gr.

If you can plan your trip for a month later it would be much better on virtually all accounts. May is the start of the season on the Greek Islands, but it will still be cool enough in the evenings for even Canadians to need a jacket. By June it will be getting hot in the Mediterranean countries, but very pleasant in the Alpine regions.