How do you accept the ugliness of blocking?

How do you accept the ugliness of blocking? I understand the title can seem a bit harsh for those who may feel offended, but as someone who has stuttered all my life and deal/dealt with severe blocks and prolongations, I just wonder how you truly accept yourself and speak freely without a care in the world. ​ Whenever I block or stammer, I start having this strange out of body experience where I almost need to zone back in. I put myself in the perspective of the other person and in most cases feel very uneasy because from their perspective, my stutter does not look/sound like what you expect a stutter to look/sound like. I don't see how anyone can justify blocking being a physically pretty sight. ​ I'm just wondering, how do you get over that fear or consciousness of the external appearance of stuttering. Dealing with the psychological aspect is one thing, but I feel like stuttering in itself is hard to be framed as graceful or unique. ​ To add, it also adds an additional layer of pressure at work where I feel like a black sheep in every meeting. ​ Appreciate any thoughts.