I've been burgled several times in recent years, and humbly, possibly ignorantly, offer a counter suggestion: consider NOT notifying pawn shops, but simply visit them routinely, keeping a low profile, in the hopes the knives will be put up for sale and you can purchase them. Depending on local laws, you may then be able to provide your proof of ownership and seek reimbursement from the pawn. Consult local laws or an attorney to be certain about recovery rights./processes.
point being, decide what you want. the thief, or the knives. I asked myself what is most realistic in these cases. Attempts to identify the thief by notifying pawn shops, though noble and the "right" thing to do, may simply make it more likely that they don't resurface in your area in the near future. Who would actually report them, detain them, and do they have motivation to do so?
Is the pawn a straight shooter, or one who would buy the knives and just leave them under the counter for a few months until the search has been abandoned? If those knives come into a shop, what will happen? will the seller be using a real id? will the shopkeeper detain them? or bother to report them, and risk alienating their highest profit suppliers? if its one of the pawn shop's regular suppliers, as may be the case with addict thieves, they might be leveraged not to report the items out of fear that the seller would roll on them and report prior receipt of stolen property. and what if the seller is reported and caught? minor charges, then back on the street. If the pawn shop buys them and turns them over to you, will they be compensated, or do they eat the loss? If they turn away the seller because they recognize stolen goods, will they still be able to get the seller's id? I sound pessimistic, but unfortunately, realistic. My personal experience with pawn shops is that a relevant percentage of their clientele may be thieves or folks inclined to purchase from thieves and then fence the items with plausible deniability through a pawn. Cooperation in recovery efforts has been non existent.
My experience, I felt that nearly everyone I would need assistance from had motivation counter to mine. Helping me would mean work or risk for them, so it was unlikely they would try. It is not an industry known for integrity and kind hearsts ( I know exceptions exist). I believe your best bet is to stay quiet until they pop up at pawn, and buy them back. then exercise legal muscle. The shop can be compelled to produce the seller's info to police after the fact, it is all logged. Thief or not, at least at that point you may have your sentimental items back. and again, you may have leverage to seek reimbursement for your purchase dollars in some states, if you have adequate proof of prior ownership and the seller/pawn does not.
I am not a LEO or attorney, so take my opinion with a grain of salt. but I've been through this a lot. So sorry for your loss and for the violation, Nandok. Trust and comfort are hard to restore. Good luck.