Bitcoin Core. In this client, it is possible to even make free transactions, or even negative fee transactions, if you want to (by using SIGHASH_SINGLE with SIGHASH_ANYONECANPAY, and specifying some output with bigger amount that you have).

Also note, that you don't need to download the full blockchain history. You can just export any transaction with 1 sat/vB from Electrum or any other wallet, open it under Bitcoin Core, and then tweak it, to achieve, what you want.

Maybe I will make some low fee transactions by myself (because who wouldn't want low fees as a user; especially if batching is not properly supported yet), but I think it would be bad in the long-term, if 0.1 sat/vB will be a new standard. Then 0.01 sat/vB, then 0.001 sat/vB, and then one satoshi per transaction (regardless of its size), and finally, free transactions would also be allowed (because by having 0.001 sat/vB, and having for example 250 vB transaction, it would take 0.25 satoshis, and it may be rounded down, if free transactions will be allowed).

And then, after next halvings, we may have a lot more non-monetary use cases, where people will make zero satoshi inputs, zero satoshi outputs, with zero satoshi fees, and then, coinbase amounts will be low, and blockchain will no longer be used to process any payments, if 90% of the network will be focused on NFTs, and other things, and if coin amounts will be treated just like some unimportant field in legacy transaction space.

Also, if transaction fees will be too low, then blocks will never be empty again. Which means, that if there will be no payments anywhere, then miners may have additional incentive, to fill block data with consensus-neutral transactions, containing unimportant data pushes, and other stuff like that.