If this is the case. Have two cryptowallets. I mean, make another crypto wallet which you'll gonna fund  but have a mixer first before transfering that to that preferred second wallet. That's the only way bookmaker will not gonna trace that address came from your orginal address.

Two crypto wallets send in one person will be the solution. Or, another solution is to  fund or cash in via shops or atm machine then send it directly to your second preferred wallet.

Though you prefer not to use conjoin or two separate wallets, those are you best options.

What exactly are you trying to accomplish? If someone gave you a unique Bitcoin address, he'll know he only gave it to you, so he'll know any funds received came from you.
Or do you want him to think/know only one of the transactions came from you, and the second transaction has an unknown source?

Use a mixer or coinjoin maybe. For example, you can use Chipmixer and use 2 chips from different addresses. If that doesn't suit your taste you can use Wasabi or another wallet that supports coinjoin.