Not impossible to rip the architrave with a hand saw. Take your time and get as close as you can, then as stevo said, caulk or fill the gap. Have you done any sawing before?
There's a small learning curve but you don't have to worry too much about the exposed edge because it should be hidden by the wall. If you can cut within a couple of mm from your guide line it should work fine, just a bit time consuming.
Not impossible to rip the architrave with a hand saw. Take your time and get as close as you can, then as stevo said, caulk or fill the gap. Have you done any sawing before?