Exactly- you don't want to re-size the axle to fit bad wheels.
How many sets of wheels are included with the kit?
You'll likely want several sets (different patterns and TPI) eventually so having a tool that will accept off-the-shelf wheels will be important.
LMS wheels are $6USD a pair.
https://littlemachineshop.com/products/product_view.php?ProductID=2972
I just measured a couple of my LittleMachineShop knurler wheels - the bore is .252. Slightly wobbly fit on the axle, which is likely what I'd want...but not .010 oversize.
Axle is just under .250 - I just measured the end and it was .248.
BTW, The LMS wheels are .373 a.k.a. 3/8" wide.