I grabbed this PNG from the internet, but I don't like how thick its natural stroke is. Is there a way to make the stroke smaller even though I don't have the raw vector data for it?
You can select the exterior of the hand (I used the fuzzy selection tool) and apply Select > Grow to select a part of the black stroke:
pressing DEL removes that part of the black which was in the expanded selection:
Better result is possible by deleting less from the outer side of the stroke and by making the white area bigger. In the next image the edge is thinned from outside 50% less, the white was selected, Select > Grow was applied and the selection was filled with white:
You must decide by yourself how much you want to cut from the outer edge and how much to expand the white interior.
The best result can be got by redrawing the shape in Inkscape - it's not a big deal when the shape is this simple (except in case one must start to use Inkscape from zero knowledge).
If the image has high enough resolution and it's free from JPG noise, tracing in Inkscape can create a good vector version. It unfortunately will have both black and white as filled areas, you cannot simply make the stroke narrower, because there's no strokes, only filled areas. But you can use Path > Dynamic Offset to make the white bigger and insert then black stroke. The original black area can be deleted. I unfortunately don't have good enough version for this route, I have only your low resolution screenshot, so I skip it.