Recreational & Family - BMX for a little kid

I have a little cousin who needs a bike. Last summer, my aunt was raving about how well she rides her bike to me (I live halfway across the country, so I didn't get to see her learn), and I asked her to show me. Well, she went and pulled out a bike with 12" wheels...that she was way, way, way too big for (she's like 9 years old now). Luckily, my aunt had a bunch of hand-me-downs from my brother and I in the garage, so I sized her on the bikes, realized she's a little big for the 20" also, put her on the 24", showed her how to mount/stop/dismount the larger bike, how to use brake levers, and in seriously 15 minutes she was riding it around like it was her primary bike. I don't know her height or inseam, but she looked very comfortable on the bike, and told me she felt fine on it. Flash to a couple months later...and my mom calls me telling me my aunt is looking for a new 20" bike for her. Apparently my aunt thinks the bike is too big for her (it's not, and she was comfortable on it when I saw her, so I have to wonder if my aunt said something to make her uncomfortable because my aunt isn't a confident rider), but it's impossible to convince her of that now. The hand-me-down 20" from my brother and me is broken (and not worth fixing, since that would cost more than the bike is worth), so she can't use that. So my aunt wanted to buy her a cheap 20" Walmart bike for Christmas. Now, I'm all for getting kids who aren't serious cyclists cheap bikes when they're going to grow out of them...but this struck me as a huge waste of money, since she fits a 24" now, which means that by the time spring comes, she'll look ridiculous on a 20" since she'll probably be able to fit a 13" with 26" wheels. However, I have an extra BMX bike that I could ship her (real BMX, not a "BMX-styled" big-box store bike). I figure that with the slightly longer TT, she'll fit it a little better, even though it still has 20" wheels. Plus she'll still be able to ride it long after she outgrows a kid's 20", if she ever decides to take up BMX. But I know she's not going to ride it like a BMX (at least for now), so I'm wondering how to set it up so she can pedal while sitting down. I plan on un-slamming the seat and leveling the saddle so she can sit on it, and taking off the pegs and putting on cheap pedals to save some weight (and because I want to keep my nice platforms haha). Besides that, is there anything else that needs to be done? It's got 175mm cranks, but there's not much I can do about that other than replacing the crankarms, which I really would prefer not to do (though it does have 3-piece cranks so if worse comes to worse my aunt can bring it to a shop and buy 165's).

Also, what's the best way to ship? I'll be picking up a cardboard bike box soon, but is FedEx cheapest? I'll be back on that side of the country for Thanksgiving, so as long as I can get it there before the holiday, it doesn't matter how many pieces it's in to ship since I can reassemble it then, as long as it doesn't include major drivetrain surgery.

Thanks!