If you really want to kill DrWatson have a look at the exe files in the System32 folder. Have another go with the MSKB first.
drwatson.exe, drwtsn32.exe.
Are you confusing DrWatson with Error Reporting which is a separate service item in Services?
Right click the My Computer Icon/ Properties/ Advanced/ Error Reporting/ Disable Error Reporting
Sounds a bit like shooting the messenger to me, have you looked at the DrWatson logs? See my later paragraphs.
Anything could be causing Explorer to crash. You could consider recent updates. Also consider any other changes you have made. Corrupted files can cause this too.
To get further information about the error look in your Event viewer.
Look in the System or Application folder. You can get to the Event Viewer via right click My Computer icon and select Manage.
Any errors logged in the Event Viewer can be expanded by double clicking on the error line.
Take any event error I.D. number and search for it on this site.
Some general things to try.
Try running ChkDsk to check your drive for errors. Right click your Drive icon/ Properties/ Tools/ Error Checking.
Run the System File Checker program from the Run Box by typing.....Sfc /Scannow in it and have your XP CD handy.
HOW TO: Verify Unsigned Device Drivers in Windows XP
If they don't work you could try repairing windows itself by running it over itself. You will lose all your windows updates but your files will be untouched.
How to Perform an In-Place Upgrade (Reinstallation) of Windows XP (Q315341)
If you want the highly technical cause of the crash look in the Documents and Settings/ All Users/ Application Data/ Microsoft/ Dr Watson/ Drwtsn32.log
Find the entry that is relevant by date and time to the crash you are investigating. The exact cause of the crash is indicated by "FAULT ->" on the left of page next to line of code causing crash. This, if your as cluey as me, wont tell you much but you can use it to see if it is the same fault all the time, and further up the log you can find what processes and modules are running.