I don't texlax/underprocess but on the relaxer instructions it will tell you the regular processing time for your hair type, so if for example regular hair (regular relaxer) and perm (straight no wave pattern left) the time is 15-20 mins, you would do half that time, so instead of 15 do 7ish, or 10 depending on how thick your hair is,
BUT this means you have to move quick applying the relaxer in only 7-10 minutes and rinsing since you wouldn't be smoothing for straightness I guess except your nape and edges.
but for every relaxer they give different times so whatever the time listed is cut that in half
Or to keep it simple use a mild relaxer or a kids relaxer.
hth