One of the best things about being a stay-at-home-dad...is the freedom of appearance without being judged.
At one of my Raleigh SAHD meetings I noticed that almost all the dads were growing beards. I can't actually grow one...so it was more of a patchy shadow after a week of neglect. We were all cracking up at our philosophy on grooming, bathing and public image. Sharing stories of how the wives were pissed that we go out of the house like that. Chances are we are going to get dirty playing or eating with the kids, so who cares. If your shirt is dirty or has food on it...it's OK...you have a kid.
Other dads could care less if you haven't shaved for three days..or wore the same shirt last time...because we are likely wearing our favorite shirt again too. If your hair is greasy with hat head or bed head...cool...we're glad you got some sleep. I take more pride in my son's appearance than my own...cuz when people stop to talk...they aren't looking at me.
In the end, you should take care of yourself...but enjoy being out-of-the-office and take the liberties while you can. The guys don't care...and don't even notice most of the time. Soon enough the kids won't want to be seen with you...even if you do shave.