Of course, Webmon is a general utility provided externally. Maybe someone has a trick so that it can recognise “cw” and choose not to alert in these cases, but I certainly can’t think how to do it.
On the other hand, why not learn CW and get all the extra points? It’s great fun, there are loads of people within SOTA that will help and teach you. It’s taken me just a few months to get from nothing to where I can do a slow speed CW activation.
You would be very welcome to join in with our QRS practice skeds in the evenings on 80m. In the meantime, the following is a superb piece of freeware that you can download to start learning the alphabet and characters, and start practising the listening. The sending is easy, especially if you start with a straight key before progressing onto a paddle.