I think there is no other wallet that supports RPC calls except Electrum without downloading the full blockchain.
I don't know exactly what you want to achieve and another thing is you are not looking for a payment gateway but it seems that you want to develop a payment solution on your own without using any 3rd party like Bitpay but I still think that you want a payment gateway that doesn't need any 3rd party.

How about check the  BTCpayserver it's not a custodial 3rd party wallet it's a payment gateway that you need to host with your own it means no 3rd parties.

However, it still needs Electrum to connect it to the hosted BTCpayserver through uploading the wallet file or through a master public key(For safety master public key would be the best).
This doesn't need so much data so it won't be a problem compared to installing Bitcoin core with full node. But the problem is if you are going to add more other cryptos as you mention above then you will need to host a full node of those coins.

All you need for guide and development of this you can find here https://docs.btcpayserver.org/