Transferring many bitcoins without restoring a seed I was thinking about how would someone transferring a handful of bitcoins say 10 or so to a new hardware wallet.

Say you have 10 coins and want to transfer those coins to a different hardware wallet but do not want to use the original seed.

How would one go about transferring those coins while being as anonymous as possible but doing so safely.  Because if you just send those 10 coins to a new address now 1 address has 10 coins from tons of different inputs. So it decreases the privacy of the account from what I am understanding.
You would want to use a mixing service. Essentially, you would send your 10 coins from your old wallet to the mixing service and get the same amount out to the new wallet. This effectively anonymizes your coins if the mixing service is doing its job correctly.

A similar effect can be done by sending your coins to an exchange from your old wallet and taking it out to the new wallet. Obviously, the exchange would be able to connect the two addresses, so it wouldn't be as anonymous.