can I switch processors?

Hi! The processors are not plug-and-play, and are physically connected to the logic boards, so it is not realistic to transplant them. Given your scenario, I would leave the working 1GHZ machine intact and buy a new DC-in for the 1.33GHZ machine. Here's the part:

[linked product missing or disabled: IF153-021]

It's not an easy operation, but the guide is on iFixit, and this way you would likely end up with two working machines, and you would not be making the 1GHZ machine unusable by harvesting the DC-in from it. A 1GHZ 12" PowerBook is still worth a couple hundred on eBay, so in my opinion it's still worth keeping it alive, if only to sell it, etc.

The DC-in is under the logic board on the 12" model, so unfortunately DC-in replacement requires complete removal of the logic board. And it's very important that you have a known-good DC-in, because you have to put 90% of the machine back together before you're able to test it, so it would be unfortunate to get that far only to realize it's still not working.