The width of the rim should not be a major concern, provided it fits through the frame and allows the tire to seat properly.

More pertinent would be spoke length. Different rims may use different spoke lengths so a drop-in rim replacement is not a forgone conclusion.

N.B. re-reading your post suggests you may be using the terms "rim" and "wheel" interchangeably. Do you have a replacement wheel (comprised of hub, spokes, and rim) available, or just a rim with no hub or spokes?

And yes, fiber packing tape can be used as a rim strip but it is not the ideal material for that purpose.