Telestrator software

I use "whiteboard" software for doing this. Plenty to choose from:

These might help you find suitable Windoze software:

Hint: If you plan to use whiteboard software extensively, think about trying a stylus instead of a mouse.

For fun, I excavated a Wacom Bamboo CHT-460 pad and pen from where it was hiding. I downloaded the required software from the Wacom site and installed the drivers. Everything worked except most of the pen features. Oddly, the touch pad worked quite nicely. I created a test image by using Microsoft Snip and Sketch, which is included with Windoze 10. Or you can download it from the Microsoft Apps Store:

Good luck.

I do that now but it's more convenient to just draw on the screen using something like a hotkey to activate it.

That might be useful sometimes, but I'm thinking of the way a telestrator works, where the lines disappear as soon as you finish looking at them.

So, press a hotkey to activate the utility, make annotations, press a key to clear it and restore normal mouse function. That would be good enough. There are some programs with descriptions that sound almost right but it turns out they don't do this.

I think I did that search. I can grab the screen with the printscreen key and paste it into Irfanview, which is fast and allows drawing. But sometimes I need to do it often in a session so it would be better to make it one step. Like press a hotkey and start drawing. Then it would even work over video although I don't need it for that. It would also work with any remote software (and I have to use various) and also work in person like if I just want to mark some objects for a moment.

I usually do the same thing you describe, also using Irfanview. However, for annotation, Irfanview is very minimalist. It's lacking in many ways mostly as a result of having only in text buffer (clipboard) and the inability to edit any added graphics on the screen. I can somewhat edit recent lines and arrows, but only with the undo feature. Irfanview was originally a photo editor, which it does quite well. However, for markup, highlighting, graphics, text, format conversion, etc, it's quite horrible compared to even the simplest whiteboard software.

After I posted my scribbling example, I dug a little deeper into MS Snip and Sketch. I soon discovered I had a whiteboard annotation program from MS Snip and Sketch as well was something similar that came with the Wacom pad. Both programs would appear at inconvenient and random times. Both had pop-up hot keys (Win-Shift-S for Wacom). They were similar enough that I was totally confused.

Anyway, I think I answered your question. Good luck.