I just say "No, Thank you!" forcefully and with pride. All you are doing is declining an offer to give money to a complete stranger and there are plenty of reasons for it. It doesn't mean you are unkind or not a nice person, just at this point you aren't going to give money to a complete stranger.
If they press you, just move on, or say "I'm not interested." If they continue: "I don't give money to complete strangers, and I don't need a <selling item>."
As for how you feel: If you care what a complete stranger that's soliciting random people on a street thinks of you, you need some new priorities. If you think poorly of yourself, recheck your values. There's something hidden that's pointing to something in your life you are unhappy about. Perhaps them asking for money is pointing out that you aren't earning as much as you could be?