Thanks for the good question!!
I must say that not only would it be inappropriate for a man to be walking through the mall holding the hand of someone not his wife but it would be inappropriate for the man to even be with the other woman in the mall.
But that is just the problem we have. If we carry the "rule of thumb" (ie don't passionately kiss someone not your spouse) to it's logical conclusion, that is, that there is very little one can do with another one who is not your spouse, then we come to the place where not only can you not hold their hand, you can't even look at them. To go that far takes us to absurdity.
But that doesn't necessarily make the "rule of thumb" absurb. Remember, we are talking about (1 what position is proper for the church universal to take based on scripture (that being the starting point for individuals to work out their own faith according to their conscience) and 2) "sensual" activity. Remember, we're not ruling out all kissing, even passionate kissing.
In that respect, I would say that it is not necessarily improper for a young man to kiss the girl he is courting on the cheek upon their parting ways. It would not be inappropriate for him to kiss his sister in this manner and on such an occasion, so, biblically speaking, how could we say it to be inappropriate for the courting boy and girl.
As far as holding hands, the Church has no grounds for prohibiting or even discouraging the activity. Individual conscience may have something to say about it according to the guidance of the Holy Spirit, but the Church has no grounds to prohibit it.
I hope this helps a bit.