There's a host of variables here to bear in mind- age, maturity, understanding and feelings.
First of all, at 13 he's likely to understand what it means to be holding his father's hand still- for most people if you think back to when this stopped, sure it may have been when they were younger, but everyone's different and this could well be the case- he could draw comfort from it still and that's why.
As for maturity, it could be that your son jsut doesn't realize the apparnt mixed meanings and implications behind doing this- but weighing this against hwo the conversation could go is important as well. As any parent will generally think, you don't want him to stop showing affection and stifle him, but conversely there does come a point that you need to realise and then say- you're a bit old for this now. The ways to say this are varied and the best judge is you on this- if he's generally sensitive and understanding then it won't be too difficult.
Understanding and feelings wise, this bears on both of you- you don't want to make him feel he's doing something wrong, or that he can't show you parental affection or seek comfort from you being around- but you also don't want someone judging you as a result of this.
I had the same drilled into me, my son had the same drilled into him in terms of crossing roads (or being near them as through a case of coincidence, both he and I frequent areas with very narrow pathways). However, as soon as we're in a "safe" area where it's ok, I made it a habit over time of asking if he'd like to walk by himself but he can hold my hand if he still wants to.
This will continue as he gets older but already, at times, he'll let go and provided it's safe to do so I'll let him do "his own thing". For my part if I were in the same situation, I would have been encouraging him to walk by himself as he's "getting older".
Then again, I'm broad minded enough that I wouldn't be overly concerned with other people's opinions as such, but developmentally speaking, he'll need to understand the societal norms and implications of being seen holding hands with his Father after a certain age.
It could well be it'll only take a few sightings of him doing this by his friends for him to realise from conersations overheard or a little joking what's going on and he'll stop doing it himself.