I'm not sure what you mean exactly by self-transfer, but I assume you are consolidating UTXOs. Every time you consolidate UTXOs an adversary can guess they all have the same owner. You are basically merging the histories of the coins together, so it really depends on where the UTXOs have come from. If they come from different sources then your privacy is reduced.
Discussion
I mean a single UTXO sent from one address to another. Just wondering if they can be used in any way to infer something about the person transacting (even if just as a very subtle fingerprint that can connect transactions or addresses).
(Probably should have been more specific in the original message)
As said by #[4], make sure to avoid utxo consolidation. Apart from that, use your own (Tor-connected) node to broadcast the transaction.
There's little new information they can gain from a 1:1: sweep. To my knowledge, the only new information they can gain on you, is temporal information. E.g. if you created a bunch of 1:1: sweeps around the same time, then they may guess all of those sweeps were done by the same entity, and thus all of those UTXOs are owned by the same entity.
Temporal analysis is a tricky beast.