Let's be clear: Loctite is not a "jazzed up latex/polymer coating". I don't know what that other stuff is, but Loctite threadlockers are cyanoacrylate adhesives with varying fillers/thickeners, different strengths, and different viscosities.
I'm looking at the Loctite catalog right now.
222MS is purple, listed as "low strength", thixotropic viscosity (means thick, like syrup).
243 is blue, listed as "Medium strength - disassemble with hand tools" - also thixotropic viscosity
248 is blue, listed as "Medium strength - disassemble with hand tools" - viscosity is listed as "semi-solid".
For the teeny screws in most saxophone work I'd go with 222. Better to have a screw gradually back out than find you have to put a torch on it to get it loose.
McMaster-Carr shows all these as currently available in a range of container sizes. For those not in the US, McMaster-Carr is a general purpose industrial supplies company, from whom everybody in any kind of technical industry constantly orders all kinds of stuff from fasteners to tools to factory supplies like oils, greases, threadlockers, adhesives, etc., etc., etc. I am sure that wherever you live, there is at least one company of similar type, serving manufacturing engineers, technicians, machinery maintenance people, prototype builders, etc. I have no idea whether M-C will export.
Be advised that CA threadlockers have expiration dates, so don't buy a whole bunch at one time. However, since they're anaerobic adhesives, having opened the container doesn't accelerate their degradation.