If it's a 9.3X57 based on a KAR length magazine you can rechamber it, but you can't load the longer cartridges into the mag. So you'd end up with a single shot or a "2 shooter".

Is the rifle you are interested in somewhere you can get pictures of it and post those pictures?
If so set a ruler on top of the stock next to the action and many of us can tell you if you have a KAR length or a GEW length action and also if it's a 98, 96 or 94 action.

94s will not be 9.3X62, but both 96s and 98s can be.

The fact that it cocks on opening means it's a 98 unless someone has done a conversion on it. If it cocks on opening and If it's 100% original it's a 98.

But that still leaves you needing to know for sure what the chamber is. Some are stamped under the wood line on the barrels. When you get the rifles take the barreled action out of the wood and look it over. That may be all you need to do to know it is really a 9.3X62. If it is a 9.3X57 I would still advise you to get it. That's a fine shell too, and easily made from 8X57 brass.