This one looks a bit tough. I would have suggested some form of adhesive applied inside and out, but the cracks are at critical points which may leak with repair. Sometimes buying a whole new skimmer is less expensive than a couple of parts, but it does not mean you have to use all of the new skimmer (assuming it is the same or similarly configured model), and you will have a few spare parts including a weir and return for future use.
Disclaimer- I have never replaced a skimmer without a liner because they both happened to be needed to be done at the same time.
I would suggest first filling the pool to about 1" of the skimmer faceplate to minimise potential liner movement.
My guess is you fear that if you remove the faceplate the liner will drop, and what you are wanting to do is keep the faceplate, gasket, liner and screws in place while attaching a new skimmer body and outside gasket. Of course, in this case you will have to back out the screws bit by bit each in turn while someone else pulls the cracked skimmer body out gradually. Similarly when installing the new skimmer body the faceplate would have to be pressed against the pool wall while the screws are each in turn screwed bit by bit into the new body. It may help to gorilla tape around the face plate (part on the face plate and on line) while doing this to assist in the liner being held in position - however, I do not know if the liner will hold up to gorilla tape removal or if residue will be left behind.
One problem might be that the pool side gasket might need to be replaced because gaskets are generally single use. You might screw the assembly tighter this time.
However, if the pool level is close (an inch or two) to the skimmer face plate, you might test to see if the liner stays in place at the skimmer so that you can replace the whole assembly. I suspect that this will be the case.
