If you want to use your router as the update client, and it only supports DynDNS, then my guess would be you have to use DynDNS. But you don’t have to use your router as the update client. You can use something like ddclient that will work with just about any service. Or some services have their own update client. For example, you mentioned NoIP. It looks like they have an update client you can install on a computer, here:
https://www.noip.com/download
Just make sure that the update client is up and running all the time. Otherwise your DNS record won’t get updated if/when your public IP changes.
If you want to use your router as the update client, and it only supports DynDNS, then my guess would be you have to use DynDNS. But you don’t have to use your router as the update client. You can use something like ddclient that will work with just about any service. Or some services have their own update client. For example, you mentioned NoIP. It looks like they have an update client you can install on a computer, here: https://www.noip.com/download
Just make sure that the update client is up and running all the time. Otherwise your DNS record won’t get updated if/when your public IP changes.