How would moving BTC from one wallet to another be private? It can all be traced on the blockchain anyway, so there is always a chance that some logs or whatever from the first transaction can be matched together - if a LOT of resources is put into it, of course!
There is a reason that hackers breaching exchanges often leave, or move around their coins without being able to cash out in fiat - there are lots of scammed people following the transactions...
Exchanging into Monero on the first device and then back to BTC on the second, completely untraceable one though - then︀ there should be NO way of tracing this!
You'd end up with BTC that you︁ can provide no provenance for of course, but that should be what you actually want︂ in this case 🙂