I don't have any wooden needles because I don't find them comfortable. I have this cutter with the blade on the elephant trunk - https://www.woolstack.co.uk/knitpro-elephant-gauge-yarn-cutter-view-sizer/ - would this be a problem?
I can avoid keeping a cutter/blade in my bag I would put a lifeline in my work and let it unravel till the lifeline.