You are correct that a low refrigerant charge is the most likely cause since you have verified air flow.
One additional check would be to see if it has a throttle valve or capillary metering system, a capillary is an inexpensive metering method with a very small tube if this kind of metering and your problem a recharge would be needed.
If there is a throttle valve it may have stuck open I have seen a couple of mid sized units with throttle valves and a tap may get it to cycle but once they start sticking they get worse with time.
I will note if R134a I have seen small 1-2 lb recharge kits at auto stores, if your system has a service port you could get a can and recharge the unit.
If you don’t have a service port there are bolt on ones that can be found on line for under 10$ but the ones I have are 1/4 flair fittings not the automotive R134a I think those are a 1/4” square thread or similar to acme and there are adapters for flair to acme that’s what I use for automotive.
I don’t know how they get away with selling the r134a but it is the real thing I checked it out a while back but the cost is quite high per pound compared to what certified people get it for in 30 lb cylinders .