I've wondered this question myself, there are a lot of places it could have come from and maybe it grew out of more than one source of inspiration. At first I thought Indiana Jones was probably the inspiration. But these days, while I don't dismiss Indie, I think it's more likely inspired by the female protagonist in the first Vampire Hunter D novel and film (which came out in 1985) she wielded a whip passed down to her from her father who had been a werewolf hunter. This taken together with some other things that really seem to be inspired by the first VHD movie makes a convincing argument to me.
Though wherever it came from the whip was a stroke of genius. Not only the delay but the length which varies with upgrades added extra layers of strategy to the game, something which would have* looked silly with a sword.
*And does with the Metroidvanias, though less so because obviously the graphics are above 8bit.