Will the "speed" of a single chainring make much difference?
Chains typically have approximately the same internal width (with very small differences so not exactly the same). The external width of a chain however varies. So higher speed chainrings for multi-chainring systems typically have the teeth slightly offset so that the chain can't "skate" over the inner ring teeth when first shifting all the way up in the rear and only then shifting to the small ring in the front. It isn't reasonable to shift that way, so in practice you can have a mismatch of about one generation in the "speedness" of chainrings. So 9-speed ring on a 10-speed system or 10-speed ring on a 9-speed system works fine.
Actually sprocket thickness for 10 and 11 speed systems is the same, 1.6 mm. For 9 speed you would use 1.78 mm and for 8 speed and smaller than that you would use 1.85 mm. So the mismatch of 0.18 mm is very minimal and shouldn't prevent operation. In any case, the mismatch is in the correct direction (too loose as opposed to too tight) so it would be very unlikely for it to not work.
Since the difference between 10 speed and 9 speed is one generation only, it's very likely to work. The absolute worst thing that can happen is that if you use some chainring other than the biggest one and smallest rear sprocket, at the same time, the wider 9-speed chain could rub on the bigger chainring. It isn't reasonable to cross-chain in that way.
So use your gears in a reasonable manner and it should work.