Your exchange appears to work nearly identically to how ShapeShift used to work until they started requiring users to create an account and complete KYC to use their services.

The lack of storing customer funds makes using your service somewhat more safe than other exchanges, although the costs, including the bid/ask spread is much higher than other major exchanges. If transaction fees ever go back to late 2017 levels, using your service will become even more expensive.

Obviously, sending money to your exchange will involve trusting that you will not take their money and run.