if you want to use bitcoin core, you have to install blockchain. maybe you can use prune mode after its totally synced.
If you want to use JSON-RPC without installing the blockchain, I suggest you use electrum servers. You can send JSON-RPC commands without installing anything. You just connect to someone's server.
the commands not the same as bitcoin-core, for instance, you can't
createrawtransaction but you can get any address balance or transaction details.
if you want to work with bitcoin-cash, You can connect to electrum bitcoin-cash servers.
check electrum protocol methods here.