[animal]

fall out of the sky.. yeah, pretty much, but …unpredictable in any single instance, but the uncertainty of befriending someone decreases relative to the number of instances, so befriending someone becomes increasingly predictable as exposure to the quantity of people you meet increases.
As far as I can see, a perfectly acceptable tactic for befriending people of certain backgrounds would be to expose yourself to "their world" and simply act as yourself. Those in that "world" who see your entry into it as positive, would be naturally attracted to you, and the possibility of positive relationships open if the attraction is mutual. Chances are, you can put yourself in a position to meet as many as you care to without the creepiness of stalking anyone, or the idea of latching on to someone because they’re a cop. You just meet them because they’re cops, if befriending one or ten "falls out of the sky", that’s cool too. Yeah, it "just happens", but it happens all the time when you’re in the right place.

Hairspray, even the old AquaNet grandma used … nearly useless for defense. That little burn is nothing compared to a good pepper spray.
A steaming hot cup of coffee handy would be lots better, but still of little value against a determined attacker, except for gaining a little bit of time..

imo …Your # 1 "weapon" is going to be reading the possible attacker’s signals (verbal, body language, etc) so that you can talk him down, back off and let him relax, get a weapon in hand and use it in time, or "exit-stage-left". While I disagree with the half-second as being likely if you are watching for signals from him, it is possible and would really suck. Having stuff handy like the pen suggestion, keys, pepper, knife, et al., isn’t gonna automatically get you out of it. These things will only give you a chance to fight back, and only then if the opportunity to use them presents itself.
If you do choose to carry a knife, and since you aren’t trained with it, I’d suggest that it would be better if he felt it before he saw it, if you know what I mean. Same with just about any lethal weapon, imo.