I'd like to see an option that makes mIRC attempt to open clicked links into an Incognito Mode browser window, where possible. I appreciate this may take a bit of detection and success is predicated upon the individual user's system configuration and choice of web browsers. Still, I believe it would be a very popular feature and follow the trend of privacy and security consciousness.

There are many tricky dickies out there trying to get users to click on links that may expose their Google account name or Facebook username if they should view or interact with the link in question. Opening in an Incognito Mode assures that users aren't logged into any platform websites that may implicate their user browsing history and raise legal questions.

I like this, I thought about it few times in the past but somehow I always forgot to ask. Nice request.

These seem to be the switches:

firefox.exe -private -url https://mirc.com

start chrome.exe -incognito https://mirc.com

A good idea, I like. This can really be relevant for security and to maintain anonymity when clicking on links.
Only I would yet proposed add to this the option to select a browser at the specified path, through that will open links on click in the windows of the mIRC client.
Note: If the browser selected in the options is not installed in the system, then the default browser should be used.

Here is an example of the created sample in Photoshop for option settings:

      

Too many options, the best one would be just to right click and have an option to "Open URL" and "Open URL in Incognito" with the default browser in use.