I know I too have a camera which was made (originally) to take reloadable 35mm. Its a Lomo Cosmic35 (same as Smena 8 but for US export). It does have a rewind knob, but their system is so mickey mouse that it is basically unusable (I'm even surprised that it doesn't tear up the film when you wind).
To use it, I asked my lab to give me an empty 35mm cartridge which I opened up using a bottle opener (it works fine). I then took the empty spool, cut the film leader off the new film and fixed it solidly to the empty spool using a strip of masking tape (going around the spool and sandwich the film on both sides to be sure).
To my surprise, it worked just fine. When I reached the end of the roll, I went to our dark bathroom (no windows) and turning my back to the door, I opened the camera back and rewound the film by hand. It worked just fine... Here are a few pictures of the monster and the inside fix
By the way, the Beirette has a great reputation for making gloriously glowing lo-fi images
[Sorry, image deleted during forum software upgrade. Please re-upload if so inclined.]