Online exchanges like ChangeNOW, SimpleSwap and FixedFloat, unless they keep records for a long period, which theoretically might be later accessed by authorities, might offer considerable privacy. I used one of these, with the Tor Browser, to exchange a coin I had bought on a KYC exchange to another kind of coin that then went to my personal wallet. No information other than the two addresses was provided to the exchange. I took a chance by not providing an email address that I might have difficulties if something went wrong, e.g. losing my internet connection, but the exchange also provided a case number and, in fact, I had no problems. Am I missing something, or does this provide anonymity to the bitcoin that ended up in my wallet? This might be something that one would not like to do with a large amount of coin, but that was not a problem for me!
Assuming you're seeking financial privacy from other network participants, yes probably. Else it depends on what kind of information access your hypothetical adversary has.
I'm not familiar with any of the three services. Cursory search seems to indicate that they are centrally operated, but some are referred to as “non-custodial”. It's not obvious to me, what said feature is supposed to entail exactly or how it is implemented, but I didn't try too hard to find out.
I did not see any indication or promises that the services do not keep logs. In fact, since some of these services advertise their great customer support, I would expect them to keep comprehensive logs in order to be able to respond to customer support requests. Obviously, nobody but the employees (or maybe even just a subset of them) can tell you what the actual internal data retention practices of these services are.
That being said, trading to another coin will disintermediate your transaction history to all but the exchange that facilitated the trade (“swap exchange”). Depending on how the swap exchange receives the deposits or facilitates the trade, the service that you originally purchased from (“original exchange”) would not necessarily know who you sent to, but especially would have almost no chance to connect it to the later payment that sent you the other currency, except perhaps by the amounts transferred and the timing or via combined information from original and swap exchange.
There are still records of:
- your original purchase at the original exchange with your full customer info
- the onchain record of the transfer(s) connecting the original exchange and the swap exchange
- the record at the swap exchange where you hopped chains
- the onchain record of the withdrawal from the swap exchange
- wallet fingerprints, transactions you made, etc. that might be linked by a sufficiently motivated sleuth
So, it does improve your privacy from other network participants in general, but depending on what your threat model is, an adversary might a) just ask customers of the original exchange what they did after purchasing there, and generally assume that you still own the coins unless you provide information that convinces them otherwise, or b) assuming that your purported adversary has access to the logs of both services simply be able to follow the path completely.