Shimano haven't been consistent over the years with the hub shell to freehub body interface, so fitting a hyperglide freehub body may not be possible, or at least not without transplanting the outer part of a hyperglide freehub body on to the inner part of your uniglide freehub body (
Youtube).
It's worth trying to preserve your uniglide sprockets because replacement cassettes are very rare.
All the sprockets except the screw-on top gear are reversible which helps a lot, and uniglide sprockets are quite a lot harder wearing than hyperglide sprockets (at least double, plus another doubling for the reverse sides of the teeth.
Fitting a hypeglide cassette onto a uniglide freehub can be done, but it's not easy - you've got to disassemble it, and file/grind the wide spline of each sprocket narrower, so it's the same width as all the others, and you'll still need the screw on uniglide top gear sprocket.
There were some hybrid freehub bodies which had hyperglide splines and both an external thread for uniglide and an internal thread for hyperglide, but good luck with finding one