I would do it in the frame with cable ties, it’s marginally more faff and you don’t have a real “centremark”, you end up just centring in the frame and making a call on where the centre should be. But that’s fine really.
Don’t fully unwind it, assuming it’s in good shape (ie has reasonably even tension and is wheel shaped and the nipples are free). Just draw it over a little at a time. The idea is to keep the wheel pretty much the shape and tension it is and not redo all that work, and just move it, like pulling on 16 ropes to pull the whole thing over.
If it’s not already got high tension I would pull it over towards the “centre” first with extra tension, then take tension out of the other side to balance, aiming to finish with adding tension (ie “pull” it to the new centre with the last step). A half turn a time is about right imo but you can go slower if you want (you can often also go faster but it’s more likely to go awry)
10mm is a huge amount though, is it definitely all correct otherwise? Ie spacers in the right place, fully settled in the frame? A couple of mm isn’t uncommon but it’d be actually quite hard to get a wheel 10mm out and not notice. In fact a lot of wheels won’t even allow it, you wouldn’t have the spoke thread available. So it’s all a bit freakish.