Next time just use a trusted service with real positive reviews like chipmixer.
IMO using a mixer isn't really worth it. I'd rather buy an anonymous altcoin and then convert back to BTC on a site that doen't require KYC but your money your choice

The OP should have checked this forum first before sending that amount. That's a lot already to most of us. At least if he encountered any issue, if he used like chipmixer, he can always post on their thread and I don't think they will ruin their image just by that amount. Anyway, lesson learned. Also, what you are suggesting is really a good option other than using mixer services. Just use a reputable exchange, anyway using that mixer services, you also have to pay a fee.