OK, here’s the dope from someone who’s spent some time as a cuffer (I was a Military Policeman in the US Army):
Smith & Wesson and Peerless are by far the two most common brands (I preferred using Peerless, but that S&W name…). The keys are the same, or at least were 11 years ago. Some US Army-issue cuffs were made by the American Handcuff Company. These were older and rather inferior and were avoided like the plague. I was issued them and bought a pair stainless steel Peerless chain cuffs and a pair of stainless Peerless hinge cuffs with my own money (~$30/pair, IIRC) to use instead (all knowledgable cops carry more than one pair).
Keys are made that fit inside “belt keepers” or bands that attach your duty belt to your pants belt to help keep the weight of the gun, baton, magazines, and handcuffs from making the dutly belt slide down to your ankles. Many officers carry these hidden keys against the off chance that they are cuffed by an assailant.
Even having a key does not make it easy to free yourself. The proper way to apply cuffs is so that the keyhole faces the wrist and the wrists face each other. Getting the key in the hole from this position requires more than a little contortion. Don’t stand over a grate while you do this; you will drop the key, several times.
Another element in proper procedure is to “double-lock” the cuffs. That is what the little nib on the back end of the key does. There is a small stud on the side where the shackle meets the lock. Push this stud in and the shackle will not ratchet any further into the lock. This makes getting a pick under the ratchet teeth impossible.
Possessing a handcuff key (or handcuffs, for that matter) is not a crime in any jurisdiction I have heard about. Possessing them in an incarceration facility, even if just visiting, is generally prohibited.
As far as the Houdini trick, that may have worked on 1920-era cuffs, but I doubt it would work today.
Speaking as someone who has been cuffed more times than your average “three-time loser” (MPs are a playful lot, especially when the beer starts to flow), including once by myself, just to see if I could get out, it took 30 minutes; it’s not a lot of fun when you don’t want to be cuffed anymore. For BDSM, stick to the toy cuffs.
Now, back to the OP: a (helpful)friend with a key.