I'd simply take off the tyres + rim tape and check the rims from the inside.
Remove any surface rust and prevent more by applying Kurust.
Also make sure the spoke ends are especially clean (+WD 40) so that you have a chance to adjust them later.
Any perforations it might be a problem, but otherwise you have stopped deterioration.
On the outside do similarly, and leave the braking surface because it will be removed by braking friction in use anyway.
Then keep an eye on it!

If you have to replace the rims you'll have to do it, but it's no big deal to do it yourself.
Just bite the bullet and try.
If it don't work out you can still pay somebody else to do it.

I haven't searched James, but one thing I do know is that searching is an art.
You need to know how to do it efficiently.