About traceability and privacy

I have funds in wallet A, this wallet is linked to a kyc-exchange from where I receive the bitcoin I've bought- and still buy.

Now I have wallet B, it's a clean wallet with no activity, yet.

Question : would it make a difference in traceability / anonymity, if I were to send the funds from wallet A to wallet B in small batches, each time using a different adress ?

Also : Is it true that, using a service like Boltz, one could easily erase their traceability by exchanging ones BTC for LN BTC, sending that to a LN wallet, back to Boltz, exchange the LN BTC for BTC again and sending those to a clean hardware wallet ?