Sure a hole saw and / or hacksaw (or jigsaw) will work well (use fine metal bits that cut smooth), just remove the PSU mobo & drives or remove PSU & drives only & seal up the mobo w/ some old clothes or plastic wrap (literally seal it up w/ masking or duct tape, isolating the mobo from the inside of the case so the metal shavings can't make contact w/ any parts) then cut away.
When finished, just use canned air to blow all the dust away then test-fit the PSU, if ok remove the wrap or reinstall everything.
Use any PSU you want, you are not "limited" to the 350w max that dell has to offer for replacement - that is the max you can get from them!
I would not get an Ultra, especially the X-connect. One of my coworkers had one die (the 500w) after only 2 months of use and was not stressing it or overloading it. seems to be common with that particular model of PSU so I don't trust them - too much of a crap shoot and you are most likely to get snake eyes.
Any one of these PSUs should do well:
SPARKLE ATX-350PN-B204 ATX 12V 2.0 350W $34 shipped @ ewiz
SPARKLE ATX-400PN-B204 ATX 12V 2.0 400W $41 shipped @ ewiz
COOLER MASTER Real Power RS-450-ACLY 450w $52 shipped @ buypc
FSP AX450-PN $57 shipped @ page
Antec TP-II 480W $72 shipped @ provantage
Antec TP-II 550W $80 shipped @ chiefvalue
In all honesty the SPI 400w (absolutely the best bang-per-buck currently on the market) should be more than good enough since it has plenty of +12v over the Dell's bestec old-school single rail design.