Generally, governments have hiring programs designated specifically for people with disabilities (cause stuttering is one). If trying for a federal job, you need to get a Schedule A letter from a doctor, speech pathologist, etc stating that you do indeed have this disability. That schedule A letter will allow you to apply for federal jobs specially designated for people with disabilities, which essentially decreases the pool of applicants and increases your chances. The schedule A letter can also help with state government jobs as well. With you having engineering experience (and an engineering or somewhat related degree I’m assuming), you could most likely get a job fairly easily because the feds are always looking for engineers.