Why do you add "while smiling" in there, I never said that. It's a critical difference, touching a girl while smiling vs not smiling. When you smile while touching a girl, that means you think the girl is 'yours', and that you have her 'in the bag' and this utterly creeps out the girl. It doesn't matter how confident you are - if you smile too much when touching a girl, it is creepy. But when you touch a girl while having a neutral expression, it means you are waiting to see what her reaction to being touched is, and that you understand that she might reject you and you won't get to fuck her. The neutral expression, the act of being perceptive to the girl's reaction to being touched, and not thinking "I have her in the bag, I am going to fuck her", is what makes it non-creepy.
Asking a girl on a date out of the blue has good things about it, like it gives the girl the opportunity to reject you, but depending on the setting it can make a woman feel extremely uncomfortable - a workplace environment is one of these settings where asking a girl on a date puts extreme pressure on her in the wrong way. And not to mention it makes things very awkward afterward if you happen to run into her again at work.
I still think my previously stated order is optimal:
1) Touch girl and see if she feels comfortable with it (and abort mission if she does not)
2) Tell the girl she is beautiful or attractive, and see if she responds positively (stop associating with her if you get vibes that she feels uncomfortable)
3) Ask her on a date
I agree that ideally it should be done very quickly after meeting her, but you should not do step 3 before you do step 1 or step 2, unless you like making life more awkward than it has to be.