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Before transitioning to the LOx tests during any new injector development, water is typically used for calculating flow rates, pressure loss, etc.
But testing with water cannot qualify as a suitable substitute for it is highly viscous than LOx. So what is the liquid that is typically suited for these preliminary cold tests?
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.
