Print your own handcuff key?
blackbag.nl
blackbag.nl
To make a long story short, such a key would have come in fairly handy at some point in my life (only we didn't have 3D printers then).
The longer story:
In Amsterdam, in the early 70's they were building a subway. This led to all kinds of bad feeling between the people and the municipal government culminating in riots on the 'Nieuwmarkt' where a bunch of houses would have to be torn down.
My dad was there when it happened and spotted a police issue pair of handcuffs on the ground after the melee.
He picked them up and took them home as a 'souvenir'. A little while later he had to go on a trip and an uncle came to look after us.
I found the handcuffs and tried them on my one hand first 'crrrrclick', ok, that was fun. Then - of course - the other arm. I showed my uncle who thought it was funny but told me to take them off.
Slight problem, they were on pretty solid, I'd pushed the ratchets as far as they would go. Now panic set in, causing my wrists to swell. My uncle freaked out too, searched everywhere for a key (which wasn't there) and finally had to call the police to get me 'liberated'.
They were definitely not pleased and after releasing me took their handcuffs with them and issued a fairly stern warning and had my dad report to the station for another lecture upon his return.
I've seen that many handcuffs can be opened with a strong, thin wire by pushing the hook, which keeps the ratchets from going back, back and pulling the ratchet out. Source was some documentation about a certain military operation where someone explained how he got out of a police station.
Think of getting out of handcuffs as one layer of security removed. There are others, which will be challenges by themselves, but I can imagine that those would be easier to negotiate when your hands are free. You also no longer stand out as a criminal with your hands out of the cuffs. (unless you were a bright orange jumpsuit of course).
Certainly, if I -- as a pretty untrained computer science student -- pick my lock in the largest new yorker police station, well... who cares? Similarly, if you pick the lock of the white house, you probably won't see the president.
On the other hand, if a highly trained marine wants to get out of some police station, he will probably get out of there, and he can raise his chances a lot if his hands are not constrained by handcuffs. (And similar, if a highly trained specialist wants to see the president, he has some chance to do so, and if he can pick any lock in the white house, his chances rise pretty much)