GM pinouts for their alternator regulators are either P-L-I-S or P-L-F-S. If you only have one skinny wire on it, chances are it's brown and on the "L," terminal. If there isn't a wire on the terminal, it's not hooked up. No secrets in the plastic connector!
Now your other options. Your current alternator sounds like it's fine and charging. Although the gauge needle might be misleading, those are acceptable voltage ranges. If you wish to upgrade anyway...
If you want to upgrade to your CS144 (because, free!), you can either buy that adapter harness you mentioned earlier (easily reversible) or de-pin your rounded connector for the rectangular one. If you have a junkyard nearby, that would be the cheapest option for finding one of those rectangular plugs.
Last option that costs a bit more...If have an internal fan on your alternator and a rounded plug, you have a CS130D. Since it's a '96, you can drop in a 140 amp AD244 alternator and reuse your current connections and have more oomph at idle - no plug changes.