Often they cut a few inches. Happy tail is a bitch to heal but once a fresh thicker tail is the tip its easier. For example most gundogs tails.
I have a male with occasionally happy tail. Someday it may need more and may need to be cut, hopefully never. If the tail gets bad enough it will get infected and rot.
Coming from a gun dog and farm dog background I grew up around a lot of dogs with home remedied tails. Super glue was one option.
It's up to you what you do. Most happy tail can heal itself but from the sounds of it your boy may have trouble.
My fosters and my own boy with happy tail have all lucky for me naturally healed.
If you wrap it be sure its a breathable wrap. Also I have seen the use of strong tapes such as duct tape to help secure a bandage. The logic behind this is fur grows back (all be it may cause further irritation when pulled out) but tails don't.
One of the best ideas I have seen but never tried is using a plastic bottle/tubing as an amor of sorts. Allow air flow of course but it will protect the tail while it heals from additional hard surfaces.
PS I did a quick search on another forum and found this.. I can't speak on it but it may interest you...
Here is what you *should* do: laser her tail. Ask your veterinarian (or call around to local vet offices) if they have (or have access to) a laser machine.
When you laser a wound it cauterizes the area and promotes new skin growth! Our hospital is lucky enough to have a laser and we have used it successfully for dogs who suffer from "happy tail".
The first laser treatment will be under anesthesia, but the treatments following the initial treatment will be done without any sedation at all since she will not feel the lasering.
Most "happy tail" dogs take about 4-6 weeks of treatments (3 treatments a week). She will wear a pretty funky medal splint at the end of her tail until treatment is done.
I wish you the best of luck!