A typical Ethereum Classic web application has two main parts. The first is the client side which is what you see when the website loads in a browser. The other is the back end or server side which is typically written in solidity and lives on the blockchain.
There are two ways I know of that you can interact with a smart contract on Ethereum Classic without the client side.
The First - Blockscout
In blockscout find the contract address for the application and then go to the write section of the contract address e.g. the write section of this NFT smart contract. All of the write functions available on the client side will be accessible.
The Second - MyEtherWallet
You can also interact with the smart contract using its ABI and the contract address. To do this: