And what if I do get a bad reaction in my little behavioural experiments? What if someone does laugh or something, as I feared they would?
The advice is to work towards not caring--
It is important to always acknowledge that causal thoughts CREATE the emotional disturbance following negative evaluation. Therefore, it is not sensible to blame the situation itself for your emotional distress. If people actually treat you badly, or make fun of you, choosing not to care is an option.
For example, let's imagine that you engage in a behavioural experiment and someone actually does laugh at you. This does not mean that you have to feel upset. What is the real cost here? If an ignorant person, who doesn't understand stuttering, reacts in a stupid way ,why should you care? What would you ever give such a person the POWER over your emotional life?