The minimum relay size is 65 bytes since Bitcoin Core 25.0. Here’s a mainnet example of a 75 byte tx (13 bytes of which is OP_RETURN data).
Doing an ANYONECANPAY|ALL signature spending to a single 0 sat, 3-byte OP_RETURN output of "ash" (“ashes to ashes, dust to dust”?) would be enough to ensure you avoid going below the 65 byte limit, and also would allow txs to be combined, for a slight saving in blockspace (23 bytes per input) and a matching slight increase in feerate.