The first thing to try might be to see if there are hotkeys you could use that wouldn't trigger the tooltip to dissappear.
Assuming that fails, a delayed capture might be what you need so that you can trigger the capture first and THEN move to show the tooltip. I will soon be adding a hotkey for that but for now you have to enable and disable the delay from the right click menu (delay time can be set in options).
You do give me an idea though, for adding a new kind of capture more that would take a bunch of screenshots in close succession, every time screen changed. That would let you capture a bunch of screenshots and only keep the one with the tooltip.
You could try using my
Automatic Screenshotter for a similar effect now. This would be especially useful if you had a bunch of tooltips you wanted to capture. The idea would be to run it, and then just trigger the showing of the tooltips, letting ASR take a new screenshot every time the screen changed. Then you could just go explore all the screenshots and copy the ones you want.