Hi, i'm new to PUA but after reading 60 years of challenge I got this ideea i'd like to try and I need your help to fine-tune it:

In the subway(underground tram) sit across a girl (the tram has to be not very crowded so you can see her and she can see you), you look at her, smile. If she smiles back (or not..you never know and I guess it's good for practice) you approach instantly:
-sit next to her and introduce yourself (the tram has to be somewhat empty...standing up while she sits it's not that good); you shake her hand, look into her eyes and compliment her "you have very soft skin/hands"

-pause for a bit while looking into her eyes and holding onto her hand (she might break the silence she might not, here i'd like some input...what do you guys think)

-tell her you have to get off soon but she looks/seems like the kind of girl you'd like to have a coffe with and ask for her number while constantly holding eye contact (if you still have her hand you can start caressing her hand)

Troubleshooting&Questions:
-what if there is no empty seat? Wait for one, approach differently?
-what do you think about being silent after introducing yourself, what if she doesn't say anything for...a long time..and pulls her hand away and looks away. If she does that was it a no good lead anyway or the silence part works after you tell her your purpose.
-If she refuses to give you her number or asks you "why should I give you my number/why should I met you" (on one hand in 60 years of challenge it says that if you hear anything besides here's my number when you ask for number she's not interested; on the other hand it says you're bound to get shit tested and you need to be persistent; how can I be persistent without breaking rapport/begging/arguing with her?
-might it be too soon to ask for a date right after I introduced myself?

I'm going to try this today and let you know how it goes, i'd appreciate your input. Thanks.