Is there any danger to the new alternator if it's not electrically connected?
Whilst I have not had direct experience of aviation alternators, you do not want to be running any automotive alternator without a battery connected. It's the main power diodes that don't like being open circuit. However, as I understand that the field circuit on light aircraft can normally be switched on/off by the pilot (unlike self contained car types), then you
may be OK if this is not energised. There is still a risk of self excitation from any residual magnetisation, but unlikely unless the engine is run at high revs. I would be inclined to earth the field terminal to prevent any chance of this.
I now await being shot down in flames from those more knowledgeable...