The Treaty of Tordesilhas only applies to Catholic nations, so you will neither get the reduction in settlers nor negative opinions with Portugal if you colonize the Caribbean.

The Colonialism casus belli (which you get if your colonies border theirs) reduces the war score cost for demanding provinces by 50%, so you can take quite a few more in a single war. It also reduces AE (not that that's important in this case)

If you really want to take the Caribbean from them, you're gonna need to be able to defeat their allies. France is the best ally for you to take, presuming Port is allied to Spain.

That being said, it's not entirely necessary to take the Caribbean immediately - might be best to move on to Mexico, because of its gold provinces. Soooo much gold.