Lost at Sea or Subcontracting
Breakdown of the required elements:
Land without being detected
Kidnap people without leaving witnesses who can identify the kidnappers as aliens
Get them into Earth orbit without launch being detected
1 is really easy. Even if anyone is watching the sky, there are going to be satellites and meteors falling out of orbit reasonably often (especially in the early post-war years) - without an active tracking network and database no one is going to identify an entering scout as an alien ship. If the aliens pick a re-entry path not visible from any inhabited area then there is zero risk. 3 is either the hardest or easiest part, depending on the technology available. If the scout ships are capable of landing and taking off without refuelling or supporting infrastructure then the only requirement is to pick flight paths over uninhabited sections of ocean to avoid observation. Orbital surveillance can tell the aliens where there is remaining habitation to avoid. If the scout ships have lower performance and require significant infrastructure then the aliens need to establish a base to support this. Details on that would be a separate question - "How do aliens secretly establish an Earth-to-orbit space program in a post-holocaust world?" However, let me observe that while you have specified that the experiments must occur on the ship in orbit, 99% of experiments would be more efficiently conducted using a remote-operated laboratory on Earth. Maybe the experiments require physical proximity with aliens who can't survive being on Earth and/or zero-gravity.
2 is very easy given the technology level described. The aliens have orbital surveillance and (presumably) the ability to build their own high technology boats / submarines or restore damaged human pre-war craft. As long as there is any maritime activity occurring the easiest solution is to use a submarine to capture the crew of an isolated boat while it is out of sight of land and other vessels. Ideally do this just as some bad weather is coming in and the families will mourn the sailor/s lost to the sea. (Note that the aliens will know when bad weather is coming in due to orbital imaging, the humans will be back to very primitive weather forecasting.)
If there are no convenient fishing or trading boats then subcontract with some slavers, assuming the aliens can pretend to be human in a minimal contact situation. Slavery has been going on in one form or another throughout human history. Let the human slavers take the risks making the capture - this also lets the aliens specify the characteristics of their experimental subjects. Arrange a handoff point on the coast, with surveillance technology to make sure that the slavers aren't being followed. The aliens take delivery, pay off the slavers with whatever will be valuable to them in the post-holocaust society, wait until the slavers have gone and transport the slaves back to their launch site by boat or submarine.
A more amusing variant, if the aliens can pretend to be human, would be to hire some adventurers to recover some pre-war technology from an isolated base. The aliens could identify the logical campsite for the adventurers to use before going into the base and capture them there. With no worldwide communications, this stunt could easily be pulled every 10 years in a different location each time without anyone wising up.
As far as actual capture mechanisms go - the aliens can either use their own "ray guns" on a stun setting or restore/copy current human options - tasers, tranquiliser dart guns, nets, immobilisation foam etc. Or send out robots with tentacles or gripping arms if a horror factor is desired.