Its certainly impossible to send such payments on a third party wallet. You can send it only using private key wallets like electrum or bitcoin core. However just sending 1000 satoshi would take you a lot of fees might even be 10000 satoshi. This makes sending such payments practically infeasible.
You can set 1 satoshi per byte. 1 input 1 output is 192 bytes. Cost 192 satoshi. Each extra input: 147 bytes. A 1 satoshi per byte transaction may take weeks to clear but what's the rush.
I sent a 1 satoshi/byte transaction last month and it took about 10 days to clear but it went through.
Of course, it requires an empty mempool and a time may come when mempool will never get empty.