Howdy.
I would say the best way in any instance is to duplicate what the factories used, and that was likely a very fast setting highly nasty industrial grade contact cement. Slap that wrap on lickety split, rolly polly with a tool, trim excess at bearing edges-etc if need be, down the line it went. Drill holes, mount hardware, bada beep..They sure weren't using Elmer's Glue. Stuff would probably kill you, from Cancer. LOL
Yep, you have to be neat, like a surgeon with Contact Cement, take whatever precautions you like, masking around the area, having some small brushes to apply, and then keep the two parts apart for a good number of minutes. A hair dryer on low may even help speed drying.
And the really delicate part, is to get that glue under the wrap, by very gently lifting the wrap, without cracking-breaking the wrap, you dig?
Then press all back together firmly, even hold for a short while.
Dry time could take 20-30 minutes.
You should be good for the next 25 years.
If you were sloppy and have excess, something like Goof Off-etc will likely remove any tell tale signs of visible tell tale glue residues.
Companies like 3M make the really good stuff, snort that stuff for 6-8 hours straight like I have many times, you will be spaced, but something like the DAP Contact Cement from Home Depot will work just fine as well.
Just have an understanding-education about how contact cements are to be used.