|The 1300 does support 533MHz CPUs.|
The M-770 should drop right in there. Like all P6-based CPUs, the Pentium M really shines on a faster front side bus, so the 2.13/533 part should give you a nice boost.
But, if you're willing to take a walk on the wild side, you could overclock your current CPU to 2.26GHz. The Pentium M pin mod forces your CPU to identify itself to the motherboard as a 533MHz FSB part. Nearly all Pentium M 735s have absolutely no problem running at 2.26GHz. I managed to get a P-M 780 to run at 2.82GHz without extra voltage on a desktop board (BIOS overclocking).
Cooling won't be a problem, as the Inspiron 1300 was built to take all models of the Dothan Pentium M, including the 2.26GHz M-780. Your battery life will be slightly shorter--at 2.26GHz, your CPU will draw 6W more than it does at 1.7GHz.
Here's a detailed guide with pics.