Welcome Ross, and any Luger is a beautiful Luger in my book. The only reason many would argue for not shooting with it is that it is all-matching (a non-matching magazine is not surprising in general).
I personally would shoot it if it were mine. However, it is not. :P It is yours and your decision should be whatever is comfortable with you (plus, you can go find a shooter now.
). Either way, you have something to pass on to the next generation and that can't be bad!
I don't generally have concerns with firing my two Lugers (a 1918 and a 1921 mismatch) but I do look for the right ammunition which will function the Luger mechanism without undue stress (many prefer Winchester White Box) though many have recommended reloading so that you can get exactly what you need at the minimum level of power you need to work the action. What a neat piece of history with the unit mark, have you been able to learn more about the unit?