I recommend to use an MWEB address as a destination in your BTC to LTC exchange to increase your privacy after exchange.
Do you offer MWEB deposit addresses for LTC?
Nevertheless, when some users ask us questions regarding BTC mixing in our support ticketing system, we always forward them to appropriate non-custodial CoinJoin solutions available on the market that we used ourselves in the past and that are proven to be the safest alternative to custodial mixers.
Thank you for the thorough response.