Petsville, I really, really sympathise - I'm missing proper exercise SO much, it makes me very achey and miserable if I don't do anything. I'm doing a lot of buggy walking, but have to be fair to DS who doesn't necessarily enjoy being loaded into a buggy and pushed around for 2 hours. Buggy walks are also fine as long as the weather's fine, but on a rainy windy day, it's not that simple. And it doesn't give me the same feeling as 'proper' exercise.
It's not just the 'getting in shape' aspect of exercise for me, it's the endorphins and the emotion. I miss the 'whoosh' of energy I used to get running, and I don't know that I'll be able to run until DS is mostly weaned, tbh. (I'm a 38FF, btw, which doesn't make the bra situation any easier.)
DS is 11 weeks now, and I did actually manage a couple of gentle gym sessions before my latest bout of mastitis, and it was SO GOOD....
I can express and leave a bottle of BM behind for DS in case he gets peckish, but even then, it's not as simple as that - I have to exercise with boobs that are as empty as can be, and be very careful with sports bras as compressing BF-ing boobs is a bad idea and can cause... mastitis! Grrr.
So much depends on circumstance - how near a gym you are, for example - if it's going to take you 20 mins to get there and 20 mins to get back, that doesn't leave you much time for exercise when you're there.
Atm I'm managing by doing yoga in the house when I can, as all I need there is a 10 or 20 min break. But I see what you mean about not wanting to do too much unsupervised.
If you can't take your DS swimming, and 6 weeks sounds young to me - I know waterbabies insist on specially heated pools for that age - could you beg/cajole your DP to at least come with you, bringing DS, but remain poolside, or in the car even, so that DS can be within reach if he gets hungry, and you have to jump out of the pool and feed him?
Sounds utterly daft, but I know I'm so desperate for exercise, I'll consider desperate measures...