Yes, using a mixture of tap and distilled water will raise gh, but also kh. Kh is ideally kept at 0, while gh for cherries at 6 dgh. Really, until you have a test kit for both, you'll just be guessing, but I'd try 50/50 mix of tap and distilled until you can get those kits.
Shrimp, even cherries, are much more picky about water parameters than fish. The best purchase you can make for that tank are those 2 test kits.