Yes you can and it works perfectly well if done correctly. You need the sprocket which can be bought and the correct spacer. For a ten speed you need a ten speed spacer. Use one from the other cassette. Are you missing the same cog from both cassettes?
If you are missing the first position you can put a spacer between the locking and the cassette to tighten up against the sprocket. The ratcheting part of the lockring and first position sprocket is not really nessecary.
It can take a bit if fiddling with spacers to get it all to work but is possible. And different sized spacers can help if you have them.
Or buy the correct cassette and use the two you have as spares. So you can change a worn sprocket with a good one. Not all the sprockets wear the same because you don't use them all the same amount.
Always check your limit screws.
I do this by pushing against the derailleur by hand into the spokes with the wheel rotating slowly. If it doesn't hit the spokes it's good.
And same on the other end.
​​​​​​Once you start doing this you can custom build your own cassette. And have the gears you want and not what the manufacturer makes which has to cover all types of riders and terrain. I use a 14/28 7 speed cassette with ten speed spacing because it's what I need.
Chain rub can be eliminated completely for any gear combo but not always. Or it can be tuned for one side and not the other.
It just takes a little bit if fiddling and thought to make it work.
Make sure the lockring is tightened into the casette and check the limit screws And nothing can go wrong.