Brilliant plan!
I'd be tempted to take it even further. Make a balloon dog, attached a string to it's neck for as a leash, place it on the floor, and then hand the end of the string to the girl and ask "would you mind looking after him for a few minutes while I nip into that store?". If she's still there when you get back from the store 5 minutes later, you'll know she's not freaked out by you and would be open to chatting and getting to know you a bit more.
As for follow up, it's hard to say.. that's got to be down to to the individual and can't be scripted. Maybe invite her for a coffee there and then if there's somewhere nearby. Just keep it fun, unthreatening, and don't worry about appearing nervous or tongue tied.
If you really "freeze up", just explain that you're quite shy, particularly around attractive girls. In my experience, most women quite like the self-effacing confidence of a man who's happy to admit being shy, rather than put on a mask of false bravado.
edit: one more thing.. All the better if the girl is with her friend. She'll be far more relaxed and open to getting to know you better if she's not on her own.
oh and if you do get to the coffee phase, tell her you only have 1/2 an hour and then you'll have to leave. This will reassure her that she won't end up stuck in an awkward situation with you, whilst also providing the perfect opportunity to tell her you'd like to see her again, and hopefully arrange a time and place to meet up. I wouldn't even ask for her number to be honest, as again, it leaves her an easy escape.
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AQ:37 FQ:105 ENTP
Your Aspie score: 141 of 200
Your neurotypical (non-autistic) score: 78 of 200
You are very likely an Aspie