Someone recommended using these in the past https://www.amazon.com/dp/B00UOTFDO0/ref=cm_sw_r_cp_apa_i_duTgBbTWE8GAF?th=1
My recommendation is to use those bags, and put all of the toys (in their own separate bags) into a big rubbermaid storage container, then buy 4 locks, drill holes into each of the sides of the lid on the container, and lock them up like that.
It may be a big hassle, but i think it would be surprisingly cheaper than buying a big enough lockbox for the job.
I have had a similar issue (though not embarrassing like yours—sorry that you had such an awful experience). Here is what I do to alleviate the issue. I bought these bags by Augbunny that I fill with bulk goods. I just write down the numbers for each bag and at check out I just read them the numbers. That helps reduce the use of the plastic ties too. The checkers love that I have it all set up for them. If they want to check inside the bags to verify, they are welcome to. I also kindly tell them to be careful because spillage is possible so keep the bags up-right (for the ones filled with grains and the like). Sometimes there is a little spillage, but never anything unbearable.
Here in Phoenix, AZ we don't charge for plastic bags like in CA. Sprouts actually gives a 0.05 discount PER REUSABLE BAG! So all my produce and bulk bin bags add up quick. Nevertheless, nobody should be doing it simply because of the savings—the environment is far more important than a few saved dollars a year.
If you type "muslin bag" on the Amazon search bar followed by the size you are looking for you should find a good cloth bag. Like this:
15x11 cloth bag 6 for $14.