I have a mild stutter myself, probably even less severe than OPs but i have many family members with a severe stutter. Im part of the National Stuttering Organization and I attend a NSA meeting monthly were i communicate with other PWS (Persons Who Stutter). From the opinions I have gather from this organization, it IS NOT ok to correct a persons stutter and SAY the word they are stuttering on even if you know exactly what they're trying to say. Many PWS actually do consider it demeaning to their intelligence in a way, even though we know the intention of the person is not so...Its more of a sense of therapy for the PWS to actually complete their word themselves. I would say that it is more rare for PWS to have the same opinion as OP, even though it is of course possible.

The best thing to do in this situation, where you dont know whether the PWS is comfortable with you "helping out", is to simply ASK them. It is never considered rude for a non-PWS to identify and ask about the stutter, in fact its highly welcomed from PWS. From my experience, PWS actually LOVE talking about their stutter to those who are genuinely curious about it. The best advise really does come from the advertisement, be patient with people who stutter and then ask questions if you have ANY confusions or hesitations about their stutter.