I've just received a positive LMO for a job that I could start right away. If I mail my application for a WP it will take likely 2 or 3 months, so I am thinking of applying for a new WP at a port of entry. I am citizen of a passport visa exempt country and I have all needed documents with me (including job offer letter and positive LMO).

My question is: is there any reason why an officer should refuse to process my application at the POE? What can I do to minimize this risk?

We have seen cases in which officers have refused to process what would effectively be a renewal of a work permit (i.e., for the same employer for an individual in Canada holding a valid work permit). There should be nothing that would bar processing of an entirely new work permit, as that is a prescribed venue.