While doing some research, came across an interesting article (Why Be a Prisoner by Houdini), where he mentions adding the famous rope trick of the Davenport Brothers to his repertoire:

I added the famous rope-trick of the Davenport Brothers, and I used to offer a prize-it was my week’s salary (fifty shillings), but I did not announce the offer in that fashion-to anyone who could tie me in a such a way that I couldn’t extricate myself. Was it a safe offer to make? Well, I only know that I always managed to keep my salary for myself.

[The Sketch 06 April 1904]

Which led to a challenge to use handcuffs instead of rope to prevent him from extricating himself:

One night a detective was in the audience. He got up and said, “I can tie you up so that you won’t extricate yourself,” and he waved a pair of handcuffs, and, as I gazed at them from the stage they looked as big as the Houses of Parliament to me, so I politely declined his offer. When I came to look at those handcuffs, however, I saw they had a lock which I could master. Remembering what I did with the burglar-proof lock, I eventually consented to have them put on my wrists. I opened the locks in sixteen minutes, and, incidentally, opened the gates of fortune.

[The Sketch 06 April 1904]

Silverman has the following take on being secured with handcuffs for the first time versus ropes:

In Manchester, New Hampshire, during the second week of November 1895, he announced that before being locked in the subtrunk he would allow his hands to be secured not with rope or braid but with handcuffs borrowed from the audience. This come-on may have marked his first public performance of a handcuff escape.

Silverman also mentions:

Houdini credited Baldwin with having given him the idea for an act made up mostly of handcuff escapes. But he credited the escape itself to Ira and William Davenport (1839-1911, 1841-77), a superlative pair of medium-magicians who ambiguously merged Spiritualism and conjuring. According to Dash, Houdini was “a great worshipper of the Davenport Brothers in his youth.”

By the time Houdini started out, in the mid-1890s, he encountered a public familiar with mediumistic handcuff tests, if not by experience at least through the press. As an 1897 article in Scientific American described them for its readers:

The handcuff test is a great favorite of the “medium.” In this test the performer uses any pair of handcuffs furnished by the audience, and by them put on him. Yet, in a very few moments after he takes his place in the cabinet, his coat is thrown out, but on examination the handcuffs are found to be on his wrists just as they were placed by the audience. As a final test, the performer comes out of the cabinet holding the handcuffs in his hand, removed from the wrist but locked.