First of all with an opener like that a false time constraint isn't really necessary. You're only asking a question so it's pretty much stating the obvious. Secondly, if you're not actually buying something then there's not a lot you can do. You can't get them to come along and help you pick something. Also, to me, even though it says you have female friends it also sends signals that you don't know what kind of things girls like.
Personally I wouldn't go with that opener at all. Think about it, you approach these girls completely at random to ask them an innocent question, you talk for a while then all of a sudden you're showing interest. Why were you hiding it up until now? Was this just an excuse to come talk to them? That's the sort of thing they might be wondering. If you start hitting on them or asking for numbers or trying to get one of the girls away from the group or whatever right after pretending not to be interested... I just can't see it working unless there's a lot of attraction there already. A lot of guys will disagree, but this is my take on it.
If your aim is just to get a number, how about being direct and honest? She may flake on you but hey, if she does that she's not really worth your time anyway... besides, for all you know she could flake on you nomatter how you approach. Don't approach a random girl without at least some eye contact from her first. Having a guy come out of nowhere can set her off balance a little. You can use the birthday gift opener in a direct way such as:
"Hey, I know this is really random but I gotta talk to you for a second... alright, I'm on my way to get a present for my friends birthday and she's meeting me in like 20 minutes so I'm in a rush. So yeah I just wanna give you a call some time and take you out cos you look pretty cool.". She'll just be like, "O... kaaayyy" and smile, it's like you're a crazy person but a cool crazy person so it's ok kinda thing. Girls like it. Hand her your phone and as she's typing it in just talk to her a little about how random this is, she'll agree and you'll get a little laugh from her. Don't learn it word for word, just say it in the way you normally talk. Keep strong eye contact with her while you talk. I always tell her she's cool and that we're gonna have fun, and give her a little smile before I move on.
This is fool proof. It's fast, efficient and they will never say no... the last thing she wants is to embarass herself or you by creating an awkward moment. It's not complicated, you don't need to think of what to talk about, you're in and out of there in just a couple of minutes and I'd say 6 or 7 times out of 10 you'll get a day 2 with her. I like to call this "drive-by pickup". Try it and see, you've nothing to lose.
CHAT