The confidence building sounds like a great idea. Exercise will have benefits from every angle. It's really positive that you feel able to take the time for yourself this way.
And well done for wearing short sleeves. Shame is a very important reason many women stay in relationships that are not good for them -- wondering what others will think of them if they make a decision to end things, not realising they don't need permission to cut their losses, or validation from anyone else for their decisions, and not really owning their own convictions, perceptions and intuition because shame (and its friends, self doubt and the feeling that you must live up to others' expectations and that you yourself are not 'good enough') leads to second guessing of themselves. Exposing your arms and saying 'this is where I have been, and so what?' is a good thing.
Try to get in touch with Women's Aid too, and see what you can manage in terms of engagement with them. In a way, having to do this sort of thing behind your P's back indicates the nature of the relationship..
You might like to get a hold of the book 'Why Does he do That? Inside the Minds of Angry and Controlling Men' by Lundy Bancroft.
And not to throw a wet blanket over things, but be prepared to see signs that your new departure and attempts to gain confidence are being sabotaged. Watch out for mess or disaster greeting you when you get in from a run, or for non-availability of P to take care of children while you are out exercising. Don't let this warning stop you from giving it your best shot however. Just take note of spanners thrown into the works. Remind yourself if P puts difficulties in your path that millions of women get out for a daily run or whatever else they need for themselves with the full support and wholehearted and generous-spirited backing of their partners, and that you have every right to the same.