Am thinking about a 1x4 leopold scope with a Hog reticle. Short weapon handy in the brush. Any ideas on this or something better ?

Respectfully

Tim In Las Vegas

I have a 2.5-10x44 Vortex on my 6.5x55 Swede that is a CZ550 Full Stock. So it's basically the same size as your 7x57.
The scope I have on it allows me to leave both eyes open on the lower power setting for close range while the 10x works well on the longer shots.

You could put a Leupold 2-8x32 on it if you are looking for something lightweight and small. I have the 1-4x20 Hog Plex and think it's not enough magnification for here in NV. Not for what I want anyways.