By "see My Fuji" do you mean just see it from a distance or actually go there?
If it's the first it is weather dependant but if you're lucky you'll get this view - taken from Diamond Princess in April 2018.
I can't recall if there were any last minute tours offered at the port. We just wandered around Shimizu on that trip. If you actually want to go closer to Mt Fuji, i.e. to the Visitor Centre, or even up the mountain to the Kawaguchi-ko Fifth Station as we did on a land tour in 2006, then it's probably best to book an excursion.