By all means check your local laws. Don't just call up the police department and ask; often you won't get good information from busy desk personel. Google up your state and local weapons statutes, and actually read 'em. Or, call the prosecutor's office.
Be aware that if you travel through several different jurisdictions, you may get different interpretations!

Here in the St. Louis area, you can easily ride through a dozen different municipalities in the course of an afternoon ride.

Self defense law can get enormously complicated. You not only have to worry about the immediate consequences of the incident, but the fact that you may be sued civilly later on.

Pepper spray is an excellent choice as in most areas it's legal (at least to some extent) and is almost universally seen as not permanently harmful. Sticks and other impact weapons can be problematic. Many statutes classify batons or clubs on their prohibited list, and they can raise the level of the incident from a "common assault" (hands, fists, etc) to an "aggravated assault" (using weapons or intending great bodily harm).
The use of weapons in self defense is generally justified if the bad guy is armed, or greatly larger/stronger than the victim, or there are other circumstances that make you feel that you are in danger of being killed or suffering great bodily harm.
The defense must cease when the assault is stopped. You cannot make the guy stop attacking you, then continue to beat or chase him. In some states, you are required to attempt to flee before defending yourself!
Complex stuff even for us cops, much less untrained civilians.