HaHa! Kwakked up, any tyre recommendation question always opens a can of worms! Everyone has their own opinion and preference.
Honestly, most manufacturers make a good sticky treaded tyre that are right at home on the track. So, you should be OK with most options.
As you are looking for a set that will offer some grip in wet to avoid the two sets of rims scenario, just be cautious with the tread pattern you choose. There are 'treaded tyres' out there that are for homologation purposes and have very little shoulder or edge tread - effectively a slick in these areas. So obviously you would want to avoid these as they won't offer any side grip in the wet.
My personal preference for a grippy treaded tyre on the track that offers some wet adhesion is a Dunlop Sportmax Q2. I stress, entirely personal preference!!! I don't mind their feel, get a decent track life out of them and offer some OK grip in the wet.
Hope this helps narrow your choice!