Next, all the shops I have been to want to cut the tip off the rod to replace the tip top. NO THANKS.
Run, don't walk away from those shops.
As mentioned, tip tops are installed with heat-activated glue if done correctly.
The original hot melt glue which is called ferrule cement in the rod building world.
Once you get the old tip top off, scrape any glue residue off the blank with a fingernail.
Then "dry fit" your chosen tip top replacement to verify correct tube size.
No massive wobble, no super tight....you're looking for an easy fit with a bit of room for the glue.
If the tube is large enough in diameter, you can cut a sliver of ferrule cement and drop it into the tube.
Heat the tube which then melts the glue and install.
With smaller tubes, heat the end of the glue stick and apply the molten glue to the rod tip evenly around the tip top area.
Then heat the tip top tube and install.
Leather or a thick glove will provide good control as you dial in proper alignment with the other guides.