Without test kits anything can be wrong with the water old or not. Unfortunately shrimp are very sensitive when it comes to water. Ph, TDS, nitrates, nitrites, gh, etc. can all affect the shrimp and cause deaths.
Sometimes keeping shrimp is like playing detective to find out what went or is going wrong. Without the test kits EVERYTHING is a crap shoot... even with cherries.
Are you using tap? If so, are you using water conditioner? Perhaps it is time for a water change.
I've sometimes blasted my tanks to top off the water to 10% a lot with tap water. It usually goes well, no deaths at all. The tap is slightly colder than the tank water, so I get some breeding from that too. I wouldn't recommend adding more than 10% with tap though. Aging the water for 3 days is always safer though. I'm just not that patient. xD
Your best bet is something like Prime dechlorinator for the tap water. You won't know if you need to go with RO until you get test kits and figure out pH. You need a master test kit for ammonia, nitrite, nitrate, and pH and then you should purchase a GH/KH test kit. A TDS meter is also good to have when keeping shrimp. Keeping shrimp is vastly different than keep something like fish and testing the water is important until you get a good handle on things.