BillieBob, 'COMMISSION REGULATION (EU) 2018/1065 of 27 July 2018 amending Regulation (EU) No 1178/2011 as regards the automatic validation of Union flight crew licences' states that the following new point (e) shall apply to FCL.045:
(e) A pilot intending to fly outside Union territory on an aircraft registered in a Member State other than the one that issued the flight crew licence shall carry, in print or in electronic format, the latest issue of the ICAO attachment, which includes a reference to the ICAO registration number of the agreement that recognises the automatic validation of licences, as well as the list of States which are party to this agreement.
I can find nothing which states that this only applies to commercial operations. Have you a reference other than CAP 1705?