There are many native and non-invasive plants which you can use in your pond that will perform the same functions as the invasive species do such as oxygenating. Ask for advise from your retailer on choosing the right plants for the size and function of your pond and make sure they will not become invasive.
Here are some suggested native alternatives for your garden pond or aquarium:
Native marginal/emergent plants
Native oxygenating plants
Native floating plants
Some other sources of advice on choosing alternative plants:
Whatever plants you put in your pond, the most important thing to remember is to dispose of them carefully by composting them or putting them in your green waste bin. You should also make sure you don’t let them escape out of your pond into the wild. You may spread plants by accident as it only takes a tiny fragment for a plant to re-grow, so do take extra care to keep every tiny piece under control by cleaning your equipment, especially your footwear, after you’ve been managing your pond.