...not really?
If your turtle is eating, he's going to give off waste. Even if he's not eating, he's still going to shed skin. It's on you for not having a strong enough filter. If I were you I would have gotten the filter FIRST.
Is this the same snapper you took from the side of the road?
feed no but you can help by adding decoro to the tank that's high in surface area like lava rock also adding plants will greatly help something fast growing like hornwort and duckweed. the turtle will appreciate the veggies in its diet as well.
ton of plants and more water volume. babies need shallow water but you could increase the square ft. plus of course water changes and trying to scoop poop with a cup