Well I try to base my answer on what my kids have shown me rather than on beliefs about kids in general. I just let my fixing to turn five year old ride his bike with me to the grocery store for fun, down a side street, crossing three busy streets (get off and push). I was nervous after we started but he took it seriously, listened well, and was glad he did it. With the details you've shared I would decide yes in your shoes (making sure to tell them about the special medicine so they know not to try it alone). Part 2, I don't know what the other mothers will say. Friends, family, and strangers alike have reacted weird to anything from my toddler or baby eating whole vegetables to climbing on the playground equipment when they're small. I'm sure they would say something about letting them watch a medical operation too. I don't know what to do about that except shrug it off. It might be better to address their concerns with stories like you've shared here, if they're interested in them.
