We are planning to go to Spain for a tour in May, also for our anniversary (which is actually in December). We will miss the horrible heat, but it also won't be cold. I am only in the research phase, but I am excited about planning this. However, we will be doing a supported tour, since I want total pampering. Several of the companies I have looked at also do self supported options.
I think you are fairly safe weather wise, with Italy, Spain, or Portugal, maybe Germany or Austria, but England or Ireland might be rainy in May.