There is no 'real man' and I hate the term with an undying passion. It's an unforgivably high standard to be a square-jawed, broad-shouldered, smoking hot, highly successful, ridiculously competent, indestructible, muscle-man with the ability to do anything and everything and do it with undying levels of confidence. I hate that standard, it stresses me out.
Just be how you want to be and try as little as possible to care. People like you who who challenge those perceptions of masculinity and (hopefully) look good doing it are paving the way for a lot more forgiving standard of beauty.