Something is wrong in your risk assessment process if you are finding new risks every day. It could also be that your risk identification was done at the wrong level of abstraction.
My guess is that you are doing this on a very low level and you should move up to understanding business impact. Risk is basically something of consequence that could go wrong. A technical vulnerability is not a risk. If you discover a new weakness in your webserver, that is a vulnerability and not a risk. The risk is, for example, that customer data could be stolen, or that your service could become unavailable.
If you view it like that, then discovering a new vulnerability would not create a new risk, it would affect the rating of an existing risk, and that is how it should be. So your server has more holes than you thought, that increases the potential frequency of loss, or whatever risk assessment method you are using (in FAIR, for example, it could reduce Resistance Strength).
Even if you uncover entirely new ways in which, say, personal data could be lost, the risk still is the loss of personal data. You just discovered a new attack path, not a new risk.
This doesn't directly answer your question, but it would solve your problem. I'm fairly certain that your existing Risk Register would serve you good enough if you thought of vulnerabilities as changing parameters in existing risks instead.