Been away from the tools for a while but I would suggest that the supposed problem here is one of definitions...
An Aircraft Installation is by definition all of the major components and the interconnecting wiring.
An Aircraft System comprises the major and contributing LRU's
The replacement of any single LRU does not constitute a change of either the system or the installation:
In fact, one could remove all of the components and the interconnecting wiring and provided that the overall configuration remains the same in terms of LRU part numbers, the installation / system remains unchanged.
In other words, by definition, you can remove, repair and / or replace the Transponder, its mounting tray, its antenna(e), the interconnect and the altitude component with like for like items and nothing changes...
Changing a transponder with a like for like replacement should have no more compliance implications than changing its antenna or re-soldering a disconnected wire on the mounting tray
After replacement I would recommend a check of the transponder installation using the appropriate test equipment to ensure compliance...
As for why your Avionics shop wont do it... it's probably all about the money, plus it's highly likely that locally they don't have the ability, the skillset, or the inclination to repair obsolete equipment.