Wheelset Cassette Compatibility Question
 

Will these Shimano WH-R501 A Clincher Wheels:
Shimano WH-R501 A Clincher Wheelset | Shimano

Work with the Shimano 7 Speed CS_HG20-7 cassette:
http://www.amazon.com/Shimano-Speed-.../dp/B007Y5HFWU

The description says Shimano 8/9/10 speed compatible so I presume not...

If that's the case, is there a way to make that cassette work with those rims?

The rims are not the issue. It is the freehub that is the problem. If you actually do want to keep the rims, you can rebuild them onto a different hub (rear or a whole set). But I suspect you said rims when you meant wheels. That is a problem.

I'm simply looking to upgrade my current wheelset and transfer my existing cassette over to the new wheels (CS-HG20-7).

I heard good things about the Shimano WH-R501's, that's the only reason I am looking into these wheels specifically.

The first question is what is your dropout spacing on the bike. 126mm or 130mm. Those wheels are most likely for 130mm.

The simplest solution would be adding spacers to the back side of the freehub until your cassette fits. Someone will know the exact thickness for the spacers.

That wheelset uses the standard Shimano freehub, so it could be rebuilt using a 7 speed freehub, then have the spacers and dishing set appropriately. I had some issues dishing a Shimano RS-10 wheelset recently as they apparently chose spoke lengths and nipples without expecting significant adjustments, so it might or might not be a problem with the R501.,

All you need is a 4.5mm spacer to use a 7 speed cassette on a 8/9/10 speed hub. I ran a set of wheels for 10 years like that. And yes a 130mm hub will fit in a 126mm spacing, even on an aluminum frame.

Cassette Spacer > Components > Drivetrain > Cassette Spacers & Lockrings | Jenson USA

Thank you so much.