You want to be below a pH of 4.2 and bring the sauce up to 195 F to hydrate / set the starch, the hold for a minimum of 5 minutes. This is your pastuerization. Then fill your jars hot (> 185) and invert to cool. 4.2 isn't all that acidic for a BBQ SAUCE. Most are below 4.0, significantly.
You most definately do need to cook anything with a pH that is higher about 3.6-ish. Even then, at pH's in the mid 3's you need to be concerned with how high the % acidity is to the % of moisture is in your formula, use pretreated low micro count ingredients, and add in preservatives to prevent spoilage.