I've named changed for this as probably recognisable.
I used to be exactly like you but (due to a combo of issues) put on A LOAD of weight in about 3 months. I ended up feeling really unattractive to men and it actually cured me of your issue.
Prior to that if I was going anywhere where their would be be "potential" men I'd make a big effort - dress really nicely, lots of subtle "perfect" make up, hair done etc etc. Probably trying too hard. Or a more refined "dialled down version" of trying too hard.
When I got fat, I couldn't get into any of my "attractive" gear and ended up not caring what I looked like. Honestly, I gave up. I became a bit depressed about how I looked and stopped caring. Once I'd got used to feeling fat and horrible, it was unbelievably liberating. I just went to things I wanted to go to (like your walking group) because I wanted to go and stopped "looking".
I felt "safe" because I knew (well I felt) I wasn't attractive. It was in this state of semi-obesity that I met a bf - because I really wasn't looking. We became friends first. And I felt really secure that he wanted me as a person - not the super-sexy version of me in my spangly sparking best state.
I can't say that I'd really advise putting on weight and (to be honest in my case) utterly letting yourself go is a healthy or sensible course but it was
very liberating.
As an alternative suggestion: How about forcing yourself to go out not looking your best? Not putting on make up or whatever you normally do that makes you feel sexy/attractive. If you don't feel that way, then subconsciously you stop that Rabbit-Ears-Up-Sniffing-The-Wind-MAN MAN MAN approach. - that is really unattractive anyway.