I own the books you're talking about (because I wanted to own the first print of DeadPool's appearance, I thought the actual New Mutants books were ass, but that's beside the point), his voice was further elaborated upon as being (I'm paraphrasing here) incredibly gravelly, deep and raspy (explained by his imperfect healing factor leaving his throat/voice box/etc horribly mangled). Though he was originally meant to be a serious character (He was a rip-off of Deathstroke at the time, but Rob Liefeld says himself that at the time he just wanted an excuse to draw Deathstroke whilst working at Marvel), writers that came later decided to make him the joke people know now, but as soon as the character began to become funny the whole idea behind his voice being like that was essentially of dumped entirely, though the speach bubbles remained.
DeadPool was taken seriously for all of 5 minutes. 5 horrible, horrible minutes.