Use json-rpc without full blockchain
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.