Yeah, if you don't have plants, then water changes is about the only way to significantly reduce nitrates. I think there is some measure of dinitrification going on in the substrate, some of the bio films, and possibly driftwood pores, but I don't imagine it's on a scale large enough to help much with water chemistry.
Plants help since they will absorb the ammonia directly, and metabolize it into tissues, removing it from the water column entirely, and bypassing the cycle.
You may be able to add things like anubias and java fern to rocks/wood. or possibly try one of the bulb plants - you can get the bulbs by themselves for pretty cheap, and just see if they manage to grow in and adapt to your tank conditions.
Another option would be to use some big floaters (water lettuce, water hyacinth, etc.), or to put houseplant clippings in (stuff like pothos, ivy, syngonium, etc.) - check the planted HOB thread for some ideas