If your JIRA team is not okay with having a webhook created, I think you’re stuck. The way the monday/JIRA integrations work, is that it creates a webhook. It just does it when you create the integration automatically.
If the situation is that the JIRA team just doesn’t want to DO it, as long as you have the required JIRA authority, you can do it. It’s a little techinical. But, not too bad.
I have not personally used the Watch Issues JIRA module in Integromat. But, this is another way to automatically create the required webhook in JIRA. Again, you would still need the required JIRA authority to create the webhook.
The document link you provided seems to give all the information needed for the JIRA side. Your Integromat person should be able to take it from there. The monday side should be no problem.