One way to bevel 1mm kangaroo thread, some possibly useful ideas you might want to try.
One of the issues when you get down to thread you may encounter is that the lace is roughly square, in this case the strand is 1mm x .82mm thick.
I tend to try to bevel this at 30 degrees leaving a spine of thicker leather on the flesh side keeping more strength in that strand.
Originally this was a 3" disk scrap from a machine, pulled thru a Aussie strander, modified with a hotel room card to stabilize the fence and allow a rough out of the lace at 1.7mm roughly. The 10ft piece was then dunked in water, wrapped around a hook once and stretched down, yielding about 14ft of 1mm - 1.5mm lace.
Then the lace was evened up to 1mm.
The goal was 3ft or longer pieces for interweaves and with the camera in the way it's very very hard to feel or see the skin side roll as pulled thru the beveling tool.
I find it far easier to use a scrap of leather, a thumbnail and a scalpel to bevel things this side but this is the y-knot tool and I'm trying to perfect the process and share the process I am going though learning it's limitations and sharing my process.
I've put a scrap of leather under the washer to help lock the blade in place.
The single edge derby blade was cut with scissors down the length of the blade, allowing for lower drag and lowering the resistance thru the blade.
single edge blades are about 1/10 the thickness of a injector style blade or of a generic utility blade. it also is flexible and allows the string to be slipped under the blade to start a bevel.