Welcome to the community
I am not sure what your asking is possible. I assume the dapps would request relayed calls with a gas price of zero, and a custom relayer would need to only relay calls to your contract, and for a recipient contract not to be funded.
I didn’t see anything obvious in the RelayHub contract that would prevent this but a quick test didn’t work in a local environment.
If you funded the recipient contract in the GSN, you could use any relayer, and you could use GSN Strategies to decide which relayed calls that your contract wanted to pay for.
Do you mind explaining why you don’t want to fund the recipient contract via the GSN?