If you have not explored Transformation/Special Effects/Bad Pixels, do so. It can be very powerful, especially for older camera sensors and if you regularly take timed exposures that exceed two seconds... ...although I have had occasions with my camera, where one or more of the more brighter Stuck pixels will show up in an image's shadow tone range with exposure times well below two seconds...
Use the F1 Help [when the "Find Bad..." dialog is 'active' in the work space] as an initial guide to get started...
As a substitute for the 'white' image, one would could simply use a New 100% white [R=G=B=100% or 255] color image based upon the raw converted 'black' lens cap image...
...for the "Find Bad..." transform to work, both the 'white' and 'black' images must be at least 24 bit color; have a 1:1 pixel to pixel registration including overall dimensions; and conversions from their respective raw files.
Illustrations...
The following scene was taken with a 10 second timed exposure using a tripod and ambient room incandescent lighting with outdoor lighting behind lightly green hued drawn curtains... ...a white 3.5x5 inch card in front of the potted plant was used as a mid-tone Color Balance neutral gray reference...

...the indicated yellow 1:1 Zoom factor 267x400 pixel image area is further illustrated: left, un-corrected bad pixels and right, PWP Raw Dialog S&N tab Average "*.badpixel" fixed...

...Stuck pixels need not be confined to the bright specks but any one or more of the R, G, and/or B channels where Stuck pixels have less than a 100% Value. These can give false colors compared to their neighboring pixels... ...shown at a 2:1 Zoom factor...

...den...