Sachs made both 7 & 8s freewheel and 8s freehub designs. They used "New Success" across a couple generations of parts in the 80s and 90s, so they can be hard to tell apart. Yours may be from before the Campy partnership (which was for 8s Ergopower). Sachs partnered with (or just bought out) several smaller Euro manufacturers before they were bought by SRAM.

If your hub has a threaded section close to the spokes on the drive side, then it's a freewheel hub. 8s (and even 9s) freewheels exist. You may be able to run a 7s freewheel if you lock out the highest gear with the "H" trim screw on your rear derailer. Or, you may be able to take out a spacer on the drive side and re-dish the wheel to run a 7s freewheel.

Here's a Sachs New Success freewheel hub, see the threaded section?

If your hub does not have that threaded section, then it is a freehub design (missing the freehub). The Sachs freehubs were apparently capable of taking a Shimano cassette. However, that doesn't mean that you could put a Shimano freehub body on there; the bearing/mounting designs are probably incompatible.

Here's a Sachs New Success Freehub, with the freehub body in place (under #6).

I have a Sachs New Success Ergopower gruppo on my Italian bike, but with Shimano 600 Tricolor hubs. It shifts the 8 speed hyperglide cassette very well (but I had to use the original 12t screw-on uniglide cog).