Under Penal Code section 16, California only recognizes three levels of crimes (Felonies, Misdemeanors, and Infractions). "Wobbler" is a slang term used to describe a crime that can be either a felony, or a misdemeanor, but a "Wobbler" is not a separate level of crime.
Penal Code section 17 describes how "Wobblers" are handled. In simple terms a "Wobbler" is a felony, and nothing less than a felony, until it wobbles. Once it wobbles to a misdemeanor, then it's a misdemeanor, and nothing more than a misdemeanor, from that point forward.
What that means, in practical terms, is that you get arrested for the felony. The prosecutor then makes a filing decision, which includes the decision as to whether the charge will remain a felony, or will be "wobbled" to a misdemeanor. Please note that the arresting LEO has no power to "wobble" the charge. If the prosecutor files the charge as a felony, then section 800 prescribes the period of the SOL. The felony punishment does not specify a term, therefore, application of section 1170(h) defines a maximum penalty of three years, thus making the SOL period also three years.
You made a good observation that the possession clause of section 32310 provides that a violation can be charged as either an infraction or misdemeanor. That kinda creates a new form of "Misdemeanor-Infraction Wobbler" that is not defined in statute in the same way that a "Felony-Misdemeanor Wobbler" is defined in section 17. In the absence of any statutory or case law defining the corresponding procedure, I would apply the same practice that the misdemeanor procedure applies until the charge is filed as an infraction.