When you click on a hotlink in mIRC, the browser which is set as windows default will open the link. If you want to specify a different browser, try putting these lines into your remote section (alt + r)

on ^*:hotlink:*//*.*:*: { }
on *:hotlink:*//*.*:*: { run C:\Program Files\Opera\Opera.exe $1 }
on ^*:hotlink:*www.*:*: { }
on *:hotlink:*www.*:*: { run C:\Program Files\Opera\Opera.exe $1 }