Hi,
there is a Jewish organiztion,the Jewish Stuttering Association, which holds suppport groups in New York and New Jersey for Jewish people who stutter. They can put you in touch with people who stutter who have successfully navigated shidduchim.
Contact The JSA
http://www.jstutter.org/contact-the-jsa/
My two cents is that you let your speech define you as a person and therefore feel that you are not likeable.
Do you have maylois that other people do not have?
Would a girl rather marry a jerk who can talk without a problem (espicaly when he is being mean to her) or nice who who stutters?
You are a whole person with defects, like everyone else in the world.
Why are you focusing on one thing and letting it define you as person?
Why do you feel you are less worthy or less whole because you sometimes get stuck on words?
Who told you that is a sin?
BTW the vice president of the USA stutters. Many very succesful people stutter.
Go for whoever you want and see what happens. The worst that can happen is they will say “no”.If you don’t try you FOR SURE wont get “her”.
HATZLACHA