I can't find an official history of the museum, so much of what I've assembled here is via two sources:
The museum opened around 1968, and I found evidence on Newspapers.com that it still existed as late as 1992. It was built and managed by Robert Dunham, an entrepreneur behind numerous popular attractions in Niagara Falls. The Dunham family had a company named Waxattract that constructed wax figures and other components. Waxattract had a subdivision named Enter-Tech.
The brochure notes: "Once you step inside the Boris Karloff Wax Museum be prepared to enter an entirely different world. A world of the supernatural ... a chilling, eerie world ... a world that will eliminate common everyday thoughts and feelings. Thirty-three different scenes will boggle your mind and thrill your senses." It goes on to specifically mention Jack the Ripper, the Phantom of the Opera, the Mummy, the Hunchback of Notre Dame, Medusa, zombies and the Devil himself.
But the museum wasn't entirely horror, it seems. You should read the entirely of the long and well-researched Reddit thread on the museum, but here's an excerpt:
"The structure the museum was housed in had formerly housed the motel restaurant and gift shop on the lower floor and suites on the top floor. The bottom floor became the museum and gift shop, and looking at old photos it appears the rooms were kept above, but cleverly integrated into a castle-like facade. ... It was the first horror themed wax museum, but was by no means a total haunted attraction. What limited photos exist in the brochures show it being fairly well-lit, and describe many non-horror scenes like Charlie Brown, MLK, Santa, Lincoln and Snow White. It's heavy animation, lighting effects, sound design, and unique theme made it a massive success."
The thread on the Universal Monster Army message board includes images of some different brochures for the wax museum. Plus images of some nifty pennants from the gift shop. Several people also share their memories of touring the museum as children. This anecdote made me laugh: "My parents took me to Niagara Falls around 1970. After a lot of begging, my parents dropped me off at the Wax Museum. As I recall, it was attached to a hotel. I bought my ticket in the lobby and looked at entry to the museum. It was all blinged out in cobwebs, skeletons, and other scary s**t. Well, I was too afraid to enter. I stood in the lobby for an hour and waited for my ride. When my parents showed up, I made up a complete description of the museum."
Writing for The Junior Reporter Club in the July 12, 1968, edition of The Evening Standard of Uniontown, Pennsylvania, young Judy Zajac shared her story about a family trip to Niagara Falls: "Both falls were very beautiful and I had a very enjoyable time. When we were leaving, we stopped at a wax museum. The name of the museum was Boris Karloff's Wax Museum of Horrors. When one enters, there is a statue of Boris Karloff. Some of the things in the museum are: The Living Heart, The Electric Chair, The Creatures, The Mummy and many more. They also had such things as Santa Claus, Little Red Riding Hood, and Snow White for younger children."
In July 1973, someone stole Dracula's red-and-black cape, valued at $300, from the museum, according to police reports. (That sounds like a good opening hook for a horror movie.)
Finally, here's a groovy advertisement from the August 30, 1969, edition of the Niagara Falls Review that describes a "ghost party" movie marathon at Hollywood Drive-In that was done in conjunction with the Boris Karloff Wax Museum.