In general your proposed process improves privacy of your coins, but it's not saving you from every way you can be tracked and it's not future proof.

Specifically consider where have you associated your "ids" with your coins and transactions, e.g. if you use WoS, then WoS company has a connection between your email, your transaction from exchange and your transaction to cold storage. The benefit is that this is not centrally and easily tracked on blockchain, but if someone asks WoS they have all this info. Also it's not future proof - you can expect that a three letter federal agency will knock on WoS's doors and ask for all the records at some point (given Canada situation, it could be in next couple days...).

So should you do this? I'd say yes until you find better solution. You should look for the better solution already :)