Duncan,
In the period between 2011 and 2015 I did four international relocations, plus two in-country relocations.
Not sure how much shaving gear you have but I had tons of stuff, to the point that it was truly an operation of respectable size to pack all these things. While I was fortunate enough to have the companies I worked for usually engaging the best removers available for the job, and to also have the service where the removers do everything for you (i.e. you do not pack anything yourself), shaving items command a lot of personal work.
So each time I literally had to pack all items myself.
Reason being all shaving items are smallish, and especially with aftershaves, perfumes and balms you do need to pack carefully. Same applies for all ceramic shaving bowls, scuttles, shaving mugs.
In the beginning I packed each and every single item in soft paper (used for removals) and also put a small piece of removal (brown) tape to keep the packing tight. I did this for practically all my soaps (lots of work). Then I threw all soaps into these cardboard boxes (medium size) that removers use. You need to be careful here, because such a box will get very heavy with these soaps. Alternatively you can use for these soaps the smallest box they will supply to you, which essentially is the box used for books - that is a strong box but doesn't offer much capacity.
Glass or plastic bottles need even better protection, and if the protection is paper then you also need to care for liquid protection, i.e. if something leaks. So at the end of the day it gets messy and heavily laborious.
As I was in a mode of pretty frequent international relocations, I had to think of something better.
So the solution I found in later years is this:
The Muji polypropylene storage boxes.
Please note that I talk about the ones with the lid on. These are much stronger, and do take wheels as well (4-stack max.)
The other pp boxes that Muji offers for storage are mostly for clothes and cannot take a lot of weight.
So you can have your shaving gear permanently in these boxes, and when the time comes for you to move, you simply fasten two or three of these well together, then have the movers put them directly into the large cardboard boxes they will supply you with.
Liquids (aftershaves, perfumes, etc.) will need bubble or paper packing but with these pp containers (and assuming you may have the original boxes of the products) you can stuff a few aftershaves in each pp container. The other 'plus' is that Muji offers these reinforced pp storage boxes in a variety of shapes, and they do have one which is tall and thin, so there you can put boxed bottles upright, e.g. a 300ml Tabac aftershave splash, next to (say) a boxed EJ shaving bowl/mug. Both safe, both don't move, and no bubble wrap needed.
I have all these at home, use them daily (all my shaving gear is in them) so I can post pictures later if you wish.
) 
