I would not drill it.
I would get a tight fitting tube to go on the outside. I would cut a slot in each end of the tube (lengthwise) so I could (hose) clamp the sleeve tight.
The sleeve should not need be too long, about 10 diameters should be long enough.
Any welding could damage the matching device in some way, if distorting insulators or flowing any soldered joints, etc. But, I'm sure the whole thing would come apart, if you were so inclined.
I would take the pieces to the welder anyway and get their professional input. It couldn't hurt to have an exspurt actually look at the pieces. They may say that a small collar inside to back the joint and a good TIG weld to be stronger than before, and they may feel they could control the heat well enough.
I've seem some very impressive TIG/MIG welding on aluminum.