I am unable to find a psu larger than 150 watt that will fit in this mini itx case. The psu inside the case is near the front of the case with a special connector that leads to the back of the case. I am fine with disabling one of the cores to free up 30 watts needed for a 6450.
The HD6450 card uses a maximum of 28w, or about double that of a 5450:
http://www.techpowerup.com/reviews/AMD/HD_6450/20.html. It is 66% faster than a 5450, and a relatively good tradeoff in regard to power/performance. While slightly overpriced right now, it's a good fit for your system, and if you need something now, this is your best bet.
A 6570 uses about 20w more, which wouldn't be a big deal if you weren't so PSU-limited. But in your case, that 20w more could put you over the edge, and I wouldn't chance it. The 5570
might work, as it uses only 10w more than the 6450:
http://www.anandtech.com/show/4263/amds-radeon-hd-6450-uvd3-meets-htpc/9. It's another 66% faster than the 6450, and thus another big jump in performance.
This really comes down to what you want to play. In modern games, you'll be giving up
a lot going down to dual core. My guess is that it just wouldn't be worth it, especially considering the loss of the third core for other applications. I'd stick with triple-core, undervolted and maybe underclocked, over a dual-core. I don't think you'll save a full 30w by disabling a core. I think this means go with the 6450.
I'd still recommend picking up a Kill-a-Watt from Newegg - it will tell you right away whether you're exceeding the rated power of your PSU, and then you can either exchange the card or disable a core as necessary:
http://www.newegg.com/Product/Produc...-001-_-Product. Was $17, now it's $20. No reason to play guessing games with your PSU. Remember it's probably 80% efficient max (maybe closer to 75% since it's so small). If it's pulling 175w or lower from the wall, you're probably safe. That would translate to about 130-140w from the PSU.