Mice do fair much better with wheels. They really love being on them! I am sure that they would be fine without one, especially if they have never been on one before, and I do know some mice who rarely, if ever, use the wheels they have. If it's noise you are worried about, then keep in mind there are many plastic wheels that don't make much noise, are easily attachable to cages, and are fairly easy to clean. There are also very small wheels made especially for mice.
And if you do get a wheel, I recommend plastic, as wire wheels have a reputation of being bad for mice due to the possibility of their getting limbs stuck in the slits and hurting themselves.
Good luck researching!
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"Heaven goes by favour. If it went by merit, you would stay out and your dog would go in."
Proud mom to Halle (dog), Sugar (cat), Tiffany (beta fish), Mango (molly fish), and Macy, Paris, Tessa, & Ruthie (mice).
RIP Kiska... the greatest...