You can pipe through a short shell script:
$ xsel -b | sed 's/^/ /' | xsel -b
The first xsel -b reads the clipboard, sed adds four spaces (^ matches start-of-line), then the second xsel -b puts it back on the clipboard. Drop the -b to use the primary selection instead (the middle-click-paste buffer).
# put two lines in the clipboard, "abc" and "123", for the example
# the \n is a newline, and echo adds another newline to the end
$ echo $'abc\n123' | xsel -b
$ xsel -b | sed 's/^/ /' # output written to the terminal
$ xsel -b | sed 's/^/ /' | xsel -b # again, to the clipboard
You can put this in a shell script, for example named "indent4", with contents:
xsel -b | sed 's/^/ /' | xsel -b
Then make it executable. You can also do the chmod by right-clicking the file in Nautilus, going to properties, and changing permissions.
$ chmod +x indent4
# test it:
$ echo $'abc\n123' | xsel -b # load clipboard
$ ./indent4 # assuming it's in the current directory
$ xsel -b # show clipboard
And then put the file on your desktop, or store it anywhere and make a launcher for it. Now you can run indent4 (e.g. double-click) and the clipboard will be modified.
xsel is from a package named, not surprisingly, "xsel"; you may have to install it. See "man xsel" for details. The $''-style strings in the example are bash-specific.