I use PCBway, and their stencils also are pretty big. Way bigger than the board. But, I had a plate with notched bars for the board to sit in, and was able to rig a hinge to it and clamp the stencil frame to the the hinge with C clamps.
Before that, I made my own stencils out of 0.003" brass shim stock, and those were made to be just about 50 mm bigger than the board. I used masking tape as the hinge. So, an unframed stencil can work fine, expecially with less than cutting-edge lead pitch on components.
I'm not sure the commercial stencil holders are any better than the thing I made up myself.
As for a squeegee, I use a piece of 0.025" thick brass shim material. It is visible to the left in the second picture. I also have a shower tile squeegee from Ikea that works, but is harder to clean.
Jon