An 8-speed cassette has narrower spacing from cog-to-cog than does 7-speed. So you'd need to either change your shifters or deal with sub-par shifting performance.
If your current cassette is hyperglide (as you say in your initial post), then it screws in with a lockring (like all modern shimano-compatible cassettes) and you can use any 7-speed cassette on the market today.
If your cassette is uniglide (in which the smallest cog also serves as the lockring and screws on from the outside) you need to figure out if your freehub is threaded on the inside as well, so it will accept a normal lockring.
I found a 13-28 7spd hyperglide cassette on eBay a couple years back, and a quick search on eBay just now revealed a
13-23 7-speed hyperglide cassette for pretty cheap.