The stock sights, both front and rear, can be removed by drifting them out of their dovetails sideways with a hammer and a brass punch. This is also how you adjust them for windage.
FYI the sight elevation adjustment ramp under the rear sight is a separate piece that is held down by the sight leaf, so prepare for it to fall out as the sight is removed.
These rifles used to be sold in a "Target" configuration with a Winchester #97A hooded front sight, #96A rear peep sight, and sling swivels. (This configuration was initially sold as the Model 68 but the company eventually made it a Model 67 option rather than a whole separate model.) However, the peep sight mounted at the rear of the receiver rather than on the barrel like the standard buckhorn open sight, and this was also the case on most other 1930s and later Winchester .22 rifles. Therefore, you can't really interchange the two sights, since the peep doesn't really work properly when it's mounted several inches farther away from the shooter's eye.
Your options are to find a vintage Winchester sight and have a gunsmith cut a correct dovetail in the receiver, or to have a gunsmith drill the correct holes to install a screw-on aftermarket rear peep sight. The second option will usually allow more precise adjustments but may require relieving the stock in addition to drilling the receiver. FWIW if you look at a lot of old .22 bolt-actions, you'll often see Lyman peep sights mounted to these guns, usually for a long-past school or Boy Scout markmanship program.
Honestly, if I were you, I wouldn't do it. Installing a peep sight on this rifle would be more trouble than it's worth and would destroy any collectible value that's left after the rebluing.
I would search out another rifle with a peep sight already on it. One can never have too many .22s.
