Granted, my experience is with diamond doves and society finches rather than canaries, but I've found that it's pretty easy to get birds to play "follow the eggies."
Our female finch laid her first two eggs in the existing finch nest (ie the "covered keet" style)... but then turned around and laid two in a "homemade" nest the finches made out of stolen rabbit hay during free-flight time in our living room. I found the eggs and gently transferred them to their nest in the cage, then threw out the hay and hid the object they were nesting in - after that, she laid the remaining three eggs in the cage.
Our two little dove pairs have been known to occasionally pick a food or grit cup to lay their eggs in and when I move the egg(s) and nesting material into the appropriate nest, they continue to incubate them. There was also a time when we wanted to switch out the existing nest for a better one after eggs were already laid and being sat on - I simply transferred the nest contents into the new nest, removed the old one and hung the new one in the same area of the cage. The birds were quick to make the switch.
If your birds are tame enough to handle, it may help to show them to the new nest... but generally, if you gently move the bird on "egg duty" out of the existing nest, they watch you like a hawk when you start moving eggs and don't realy need the escort . The only time I could see it not working to move their eggs to where you want them to nest is if you're trying to switch between a covered nest and an uncovered one since most species seem hard-wired to prefer one or the other (for example, fiches love the covered/doves want an uncovered).