In Photoshop you can make a layer mask from transparency:
Now you can select the mask icon in the layers panel and apply curves to it:
This curve keeps fully opaque and fully transparent areas intact.
You can make the shadow smaller by painting black on it in the layer mask. As well you can select the shadow with the magic wand and delete it. Then you can make a new. Photoshop's layer style Drop Shadow is a way to do it fast.
You have different possibilities in GIMP, where transparency is as adjustable as RGB channels and you can combine selections which are made by using different criterias
The same example:
In GIMP it's possible to adjust transparency directly with the curves tool. One adjusts alpha channel instead of colors:
This curve keeps fully opaque and fully transparent intact.
As said, partially transparent areas can be selected and deleted to fully transparent. One possibility is to use the Fuzzy Selection tool (=the magic wand). Its tool options can be opened by double-clicking the tool icon. By setting parameter "Select by" = Alpha and turning the treshold (=capturing tolerance) low, say =5, one can select the opaque areas. Inverting the selection and pressing DEL kills those areas which aren't nearly opaque. Then it's the time to insert new drop shadow.
But if there happens to be faded edges of other colors than the black shadow? For ex. curved edges have partial transparency for antialiasing in all colors. Removing transparent parts removes also the anti-aliasing and makes the edges jaggy. That's fixable for other colors than the drop shadow color. One can for ex. select at first transparent enough areas. Then he makes selection intersection with those areas which have the color of the drop shadow.