Yes. Privacy of a DEX is highly dependent on the implementations of the tokens being swapped as well as the DEX design. There is a concrete proposal from Qedit (ZIP 228 — Zcash Shielded Asset Swaps) on how to support atomic swaps between ZSAs, optionally via a matching service. We have taken that design into account when specifying ZSAs and sighash versioning, to allow it to be deployed as easily as possible after ZSAs. (If ZSA support is split into its own upgrade, as seems more likely now, shielded asset swaps might be deployed at the same time depending on a governance decision.)
That mechanism maintains as much privacy as possible even against the matching service, and it is completely atomic. No party has custody of the assets at any time, other than the intended custody of the swap participants. The result is a much smaller attack surface than any cross-chain DEX —private or not, ‘trustless’ or not— and that at least matches the attack surface of other intra-chain multi-asset DEXes.
I don’t think a Zcash Custom Asset that directly attempts to “wrap USD” is at all likely to be deployed. Maybe we will eventually see one that wraps USDC, USDT, etc. (if the regulatory environment becomes more amenable to that), but I don’t see the issuers of those tokens cooperating any time soon. And that’s fine IMHO.
See this post for a possible alternative: prices denominated in USD or whatever the parties are comfortable with, but paid in ZEC.