OK then, fair enough.
YY to Connecta, but at 6 weeks you'll probably need to cinch the bit that passes between her legs using the chest strap that comes with it, as it will give her too much hip-spread and go past her knees. You'll probably need to do this until 9-10 weeks, depending on her size. It will last you well into toddlerhood, however, so you get your money's worth. I could still show-horn my two year old into if up until a few months ago and he's huge.
The other go-to, which is the nearest you'll get to mimicking the position you're aiming for a wrap, without the human macrame, is a Close Caboo. They're not much good past 4-6 months, however, so while the positioning is probably better for a newborn than the Connecta, you won't get quite as much bang for your buck, although re-sale on them is pretty good.
The £28 Mothercare sling mentioned upthread doesn't give the advised M-sit position at the hips, so I'd steer clear of that one for ergonomic reasons. The sling should extend from knee-pit to knee-pit securely under baby's bum, and for the full length of both thighs. If the sling doesn't do that, avoid.
Since you've not been able to visit a sling library, I've attached TICKS for safe babywearing in case you've not come across it before.