I don't have a severe stutter myself, but like you, when I'm nervous I tend to trip over my words and struggle to pronounce similar-sounding letters next to eachother (getting me to attempt a tongue twister is a no-no!) In my line of work I actually do a whole lot of public speaking! Initially in the very early days of starting my then 'new' job, I used to tell people that I was nervous and ALL of them were all super supportive and understanding. Now, nearly five years down the line, I stutter often, but the public don't seem to mind at all! I've only ever had one person who insisted I explain something again but this was not out of malice, or at least I hope so! You would be surprised how many people do have a stutter, even just a small one only caused by Anxiety. My answer would be that it's completely up to you whether you decide to tell others. If you fear judgement, I can easily reassure you that people really don't mind all that much, at least in my experience! After all, it's nothing to be ashamed of!