Not all free advice is good advice...even though well-intentioned...
Many (not all, of course) moving companies are like car salesmen...you get my drift... count your gold fillings before and after you deal with them.
I've had thousands of dollars worth of stuff lost, or damaged beyond repair (a Honda Gold Wing bike) in two past moves. One Arkansas mover said his company employees begin every day at 8 a.m. with a prayer. They were just praying for good stuff to steal...
If you use one, purchase an independent insurance "rider" to cover your contents...as "replacement value." Take lots of pics. This info just came from ClarkHoward.com...a great Christian radio host who sells nothing, but advises callers how to save money and avoid being ripped off by scams. He is excellent; have listened to his Sunday radio broadcasts for many yrs.
Wrap all of your knives well; put them ALL into one or two USPS Priority large flat-rate boxes... each box can contain up to about 80 lbs of stuff. (I don't know how large your collection is...) Tape it closed and label it. The postal clerk will ask you if it contains...explosives, gas, and dangerous stuff...you just say no... I usually tell 'em pocket knives.
Then register and insure the box for as much as the knives are worth...or more... Make sure you have pics of every knife that goes in, and take a pic of the labeled box. ...important "just in case." This box has to be signed for at each and every postal location that it passes through...it will be safe..
I have shipped or received several hundred boxes (knives) in USPS small flat rate boxes...or just in USPS regular mail (small boxes or in padded paper mailing envelopes). NEVER a loss, except when I dropped a USPS box into a FED EX "barrel" and it "disappeared." That $400 knife was never seen again...by me.
The Fed Ex supervisor said that his pickup guy never saw a box in the FED EX drop-off container. Surely, he has very bad eyes, and a very nice knife.
Just note that coin dealers ship gold and silver coins and bullion in much the same way...by USPS.