Why? An edged weapon that'd have a moderately large contact area is definitely not what DF considers a whip.
Definitely? No. It's hard to say what DF considers a whip because what DF considers a whip breaks through God-metal.
Except that we don't have descriptions of whips at all. We might have it entirely wrong and DF whips actually look like chainswords. Which would kinda make more sense.
Regardless of the whips' structure, style or design, the raws give us some insight into the nature of whips in vanilla DF: they are blunt weapons with a contact area of 1 cm, size of 100 cm^3 and a velocity multiplier 2.5 times that of all other blunt weapons in the game (with the exception of flails, which being a chain weapon themselves are apparently modeled similarly). So regardless of whip performance in game, we can say with assurance that they are closer to a chain whip than an urumi.
Due to the ease of modifying the size of whips (by altering the [SIZE] token for them in item_weapon.txt -- they're the first weapon on the list in vanilla raws) and the well-supported case that this change would manipulate the game mechanics in a way appropriate to creating a more realistic simulation, I recommend this change as a solution to the current whip overpower problem.
Additional question: is the "penetration size" attribute measured in centimeters, or what? If it is, then that value should be changed in the raws as well: even against skin, a metal whip wouldn't penetrate to 2.5 inches deep. Presumably.