Big Bang mini is too short and isn't all that great IMO. You drag around your ship with the stylus to avoid fire. You also use the stylus to shoot fireworks at crap on the top screen. It's not very accurate (the touch controls), isn't really fun or challenging, and iirc some of the bullets kind of blended with the background. There are better shooters on the DS. If you can, check out Ketsui Death Label, if you're into bullet hells or danmaku, it's Japanese only, but it's pretty good for a challenge. Short as hell though.
If you're getting like one or two games, I'd pick up Platinum since you don't have any of the other Pokemon DS titles. If you're looking for something that'll take you a long time I'd also look for Disgaea if you haven't played any of the other versions. awp will probably bitch that the DS version is inferior, which it technically is because some voice acting and musics were cut out to save space on the little ds cart, but the game is absolutely the same, and the replayability is great. If you don't like strats or a bit of grinding once in a while it may not be your cup of tea though.
I actually just got back from a trip and I spent the majority of the time playing GTA Chinatown Wars, Pokemon Platinum, Henry Hatsworth (Great game, challenging too, I dunno if it'd last you 48 hours though), Avalon Code, Fire Emblem (The new FE1 port to the DS) and this European game release called Enchanted Folk (it's Animal Crossing-like so I only played it like twice a day). Although I have a Flashcart so I pir8ed all that stuff (and more too, didn't have enough time to play them all =3)
Also may look into FF Tactics series, Advanced Wars Series, Tetris (between short periods of time, seriously I have sooo much time on my Tetris DS just from in between lunch line at school and such. And, honestly, you could kill a lot of time with the new Yu-Gi-Oh release if you're willing to play it. Those are really well made games, they don't get the attention they deserve, Yu-Gi-Oh is really fun, I don't care what you say.
If you're looking for shorter titles look at Bangai-O Spirits (Google it, it's different), Contra 4 (
Hardest Game on DS 2D shooter), Metal Slug 7 (2D Shooter), Yoshi's Story DS (Platformer), and Etrain Odessy (2) (RPG) for hardcore challenge. Lunar Knights (Action RPG), Mario and Luigi series (RPG), Megaman Starforce Series (RPG), FF IV (RPG) for RPGs. Bleach fighting series and Ultimate Mortal Kombat for fightan. Pheonix Wright for awesomsauce (No replay value though
). Mario Hoops 3-on-3 (
Sports? fun), Dragon Quest: Rocket Slime (Adventure?), RE DS if you can fined it (Survival Horror), Jump Ultimate Stars! (Japanese fightan), and Daigasso! Band Brothers DX (Japanese Rhythm) for other.
There are tons more but I realized this post looks dumb now. You should just get a flashcart really. Especially if you are even considering things like Big Bang Mini. Try before you buy.
PM me if you have any flashcart-related questions or questions about other DS titles you may be interested in. Or just tell me what genre you want and I'll point to good games.
EDIT: TWEWY is really good, but it won't last you 48 hours unless you're awp. Also Layton is good, but has basically no replayability once you've solved all the puzzles.