create the graphic (symbol) in photoshop (ps elements is okay) or other such application. save as symbol.pdf. then open symbol.pdf and target.pdf in acrobat. using the 'touch up object' tool save the symbol (to clipboard); then bring up target.pdf and paste. position and adjust symbol as need with 'touch up object' tool.
Your post got me thinking. What about using Window's Character Map? Populate a 'source' file with the characters you want. Create the PDF. Then, using the TouchUp Objects tool as you describe, use this "character-premier" PDF as the "pick list".