I know this response is a bit late but i am also in the same boat. I finished university a few months ago and I do not yet have a job, I also have a stutter that ranges from mild to severe depending on the circumstance i am in. I've gotten a lot of advice about jobs and what i've gathered so far is that networking would be a great advantage. At this point if i stutter badly so be it, i am tired of my stutter always ruining things for me. People have challenges and this is my biggest one so If hiring managers are really interested, they'd not focus on my speech but rather on what i can bring, that's the mentality i want to have going forward. Would it be easy? no, would i be looked at in funny ways during networking events? probably, but what other options are there? applying for jobs behind a computer only does not yield results