Fitting 7” wheels to 6” Rain Tires?

I have a club race this Saturday and there’s a 45% chance of rain Tuesday Friday Saturday . I have a never really had a reason for rain tires till of course, now. I have two sets of wheels and each is 7.75” wide with the slick tires being 7.1” wide . The MG rain tires I’ll need to run will be 6” wide. Do I need to buy new wheels as well or will the wheels I currently run be able to hold the 6” wide tire?
This is just for the rears FYI, the fronts will fit

Pretty sure you will need rear wheels.
Might make sense to grab some cheaper aluminum rain hubs.

You can mount them up. It won’t be ideal for handling, but it won’t hurt anything to do it.

I’ve got a set of 6" rain tires mounted on a set of 210 mm wheels. You can do it, it’s not the easiest to get them to bead since there is a decent gap, but it will work. Just run higher pressure than you would on a slick.