I'm assuming that you want to get it done in a day.
I was figuring a weekend rental. That would give me two days, but the rental could spill over if I need more than eight hours running time. What I really want is to buy something like an old Bobcat 325, but I would have to figure out how to convince my better half that I really need this to do all the little landscaping projects she has.

I thnk you might be pushing it with the smaller one, depending on how much work you have to do on the other pond, and how far you want to move the dirt that you dig out.
I would be using a lot of the dirt to fill in two low areas just a few feet away, and loading the rest on my dump truck to start a topsoil pile.
The smaller fish will like it, but how will you keep the LMB out? I've had them swim in 4" of water to get to a small pool like you describe, then swim back out for deeper water if I walked up.
I was thinking about a small dam or just a small pile of rocks in the existing stream bed, so the water from the branch would have to flow over or through the rocks. That's the part that worries me. Not sure it would work.
I figured this subject had probably been discussed previously, but I haven't found anything yet.