The total population of earth as of today is around 7.3 billion, of which about half are men or 3.65 billion (since I suppose we're only talking about male shavers), and of those about 80% or 2.92 billion are of shaving age.
If we would agree that total regular shaves via a non cartridge razor, including a straight razor, or a non-cart single or multi blade razor (including a piece of obsidian, a hunting knife, electric razor, a real barber shave, a user-friendly blowtorch, an axe and/or depilatory powder or cream) accounts for no more than say 15% of total shaves (being generous) equaling 438,000,000 persons, and throw in another 15% or 438,000,000 more for ape men-type guys who never shave, (again being generous, but I've seen some in the subways), that equals combined 876,000,000 non-cart shavers and apemen, or about 30% of the total population of 2,920,000,000 potential shavers. This means a full 70% of the male shaving population, or 2,044,000,000 shavers are using a cartridge when they shave.
So I guess the answer to your question is yes.
Respectfully yours,
Hidell
Just guessing here, but I'd assume that in non-first-world countries, where the majority of people live, the percentage of non-cartridge shaves might be considerably higher than 15%.