I think in case of SEM, it is quite touch to observe directly hollow structure like your case. As i know that a focused ion beam (FIB) combined with SEM is used to observe cross section of fiber such as carbon nanotube yarn (look like fiber with smaller diameter). But that method is quite expensive and I don't know how to do that. It is better to check literature. Moreover, I am not sure but u can try indirect way by surface absorption measurement. I don't know in detail but I hope it can help u.
My suggestion is try collect sample certain thickness and cut the carefully with a surgical blade in a single cut. I think this will help u.. even though it depends upon your polymer property.
Keep the nanofiber mat in between the double sided cellophane tape, and cut it using surgical knife. Now very easy to cut. If your polymer withstand the heat means you can apply wax instant of double sided cellophane tape and cut it using surgical knife
I fully support the idea of using liquid nitrogen. However, sometimes certain polymers are not getting frozen in liquid nitrogen(LN) (for instance: PLLA nanofibers get swollen in LN instead of getting hard and frozen). I saw many SEM images of nanotubes cross sections, so try. Maybe you will succeed.
Also, idea of applying the tape is quite useful. I saw that technique in membrane cross section analysis in SEM. It is easier to put the sample in proper orientation in SEM chamber when you use tape or wax.
I used transparent epoxy resin using small biological containers to make composite with nano fiber yarns. Then used microtome cutter to get thin slices. I could get good images from these slices.
otherwise use any available dye in polymer solution to get colored nano fibers. then use confocal microscope to get images of different color to get better idea of hollow fibers. Depending upon the type of confocal available, you might be able to construct a 3D image up to a depth of 100 micron.