Should my SOP mention self-funding?
I'm not sure why you think you need to be subtle. 


  "My savings and investments are sufficient to carry me through a long period of study if necessary." 


That demonstrates some serious commitment on your part. I wouldn't put any financial details in it and doubt that it would be proper to ask for them. 

Or add "with only minimal funding" if you want to not let them off the hook too easily.