Sutton (7th edition, but the only one online) says
Hydraulic and pneumatic components (valves, pipes, expansion
joints) can readily be water flow tested on flow benches and
corrected for pressure drops and density (and sometimes also
viscosity) to determine their pressure drop at rated flow.
The fairly in-depth book The Saturn F-1 Engine mentions only water flow testing for the F-1. There is a nice picture of an injector test.
It appears that some small scale facilities(3 lbm/s) have used LN2.
I couldn't find anything on similarity correction for injectors specifically. This paper discusses it for turbomachinery:
Traditionally, in scaled water flow turbopump testing, it has
been considered sufficient to match flow coefficient and
cavitation number, which are the key fluid mechanical
parameters for cavitation similarity. Strict Reynolds number
scaling is deemed unnecessary in rocket turbopump testing as
these pumps operate at very high speeds in the fully
turbulent regime (Re>10^6 ) where Reynolds effects remain relatively constant.