Greg, I'm not familiar with toyota trucks, but if the radiator is built like a GM is, you can definitely use an automatic radiator in a stick shift truck. I would assume the automatic radiator might actually be a little larger/thicker because of having to also cool the transmission through the coolant, where the stick radiator would have less thermal load. just an assumption on my part though, no actual knowledge.
This link suggests the radiator could be interchangeable:
https://www.partsgeek.com/catalog/19.../radiator.html
Some of the listing do differentiate manual and automatic, some don't.