What is required to recharge refrigerant in a built in ICE CAP Air conditioner that cannot be moved?
Air conditioners do not magically lose refrigerant.

If refrigerant is missing, the air-conditioner leaks; if the leak is not fixed, it will continue to leak. Fixing the leak is a related service that you absolutely require before you even think of adding refrigerant or having anyone else do so. Since you quite obviously are not equipped to find and fix the leak, you need someone who is both trained, equipped, and in the USA (at least), properly licensed.

It is HIGHLY unlikely that the air conditioner cannot be removed. The HVAC tech you are afraid to hire probably will know how, or be able to figure it out. That might let you replace your old, leaking, likely inefficient and requiting expensive old refrigerants A/C with a new, efficient, non-leaky and using far less expensive refrigerants unit, if you chose to.