Taylor might actually be really good practice for that actually. If he can come up with a maintenance procedure simple enough a High school Sophomore can figure it out, surely that's good enough, right?
But yeah, can definitely see him getting bad flashbacks to Yinsen, to the point that he might even try to get her some very low profile body armor, which is ironically just about the only thing she can do better then he can.
Actually, random thought- when Taylor tells Tony she can weave spider silk, he may suggest she mass produce vests in an attempt to keep her from fighting. And from there, may suggest she start a line of Spider Silk clothing to protect people in their day to day activities, and make lots of money at the same time. At which point they're going to need a fashion designer who can work with Capes. Because bringing in Parian early would be fun.