The vast majority of professional balloon sculptors choose to use pumps (either small hand pumps or portable electric ones running on rechargeables) in order to spare themselves the unneccessary constant pressure on blood vessels and lungs. I have several of both types. Anyone who has problems with migraines should definitely avoid blowing them up by mouth. One also increases the odds of developing a latex allergy or inhaling too much talc over time. Obviously I’m referring to those who do hundreds or thousands of balloons as part of their working schedule not someone using a handful for a celebration.
The skill for which one is being paid is NOT inflating the balloon. Anyone or anything can accomplish that with zero skill level and it proves nothing other than a desire to appear macho.
The real skill is in the vast number of creations that are made once the balloon is inflated. That’s why they’re called balloon artists :)
If you value the blood vessels in your eyes and not raising your blood pressure unnecessarily, spend the $5 for a hand pump if you plan on blowing up more than one or two of these.
Also, the more you mess with weakening the latex, the higher the incidence of pops or quicker deflation from air escaping.
But whatever you decide, have fun !