I think that using the "Save as..." and navigating to select the external drive desrired location should do the trick. After checking that loading that new project works fine, you could simply delete the original version.
For perennity sake, I would also consolidate
the project before moving it.
LogicPro 10.6 ( & 9.1.8),MainStage3.5
MBPro 17", Core2Duo, 8G, OSX 10.12.6
MacPro, Xeon 6Cores, 64GB, OSX 10.15.7
ULN8, MOTU MIDI TP-AV, C4, MCU Pro, KorgNano, Novation SLMkII
AAS, NI, Celemony, Spectrasonics, Korg, etc...
PC, iPad3(V-Control & LogicRemote), AtariST(Notator SL), Several vintage gear