Part FCL Definitions:
"Pilot-in-command" (PIC) means the pilot designated as being in command and charged with the safe conduct of the flight.
Part NCO:
NCO.GEN.150 Journey log
Particulars of the aircraft, its crew and each journey shall be retained for each flight, or series of flights, in the form of a journey log, or equivalent.
however the owner said that as I am not a shareholder I am not able to sign the tech log.
There is no requirement to sign the Journey Log so that is not an issue. So long as you are qualified and
"designated" there is no problem.