I personally would have more headspace than 1/4" or a bubble the size of a Skittle. A few mL is what I do, not because of expansion in the freezer, but expansion if the bottle is put into a warm environment. If you fill the storage bottles in a cold kitchen in the winter, leave virtually no headspace, then bring the bottle out into a warm room in July, you could get some leaking upon expansion of the liquid. I have.
The amount of O2 in a few mL of headspace is negligible compared to the amount probably already dissolved in the VG or PG, especially with larger volumes. Can't do away with that, but it is also negligible, and will not react anyway to any significant extent in the freezer. And even if it all reacted, you would be hard pressed to be able to measure or detect a difference if the bottle was sealed.
I like these bottles for storage and syringe dispensing during use.
Specialty Bottle - Amber European Dropper Bottles
The Eurodropper inserts act as a gasket during storage, and syringe access through the center during use after I bring a bottle out of the freezer. Spill-proof too. I use 50 mL bottles, bring one out for some weeks of use. I don't usually put partially used bottles back in the freezer. Plastic is porous and will allow O2 to enter through the wall of the bottle over time. Not that that is a bad thing, oxides can actually add a nice flavor. But glass does very well even at room temperature for quite a while.
Almost at 5 years now for some of my stored nic in the freezer, and no changes that I can detect at all.