First, a caution: This is wiring for higher power levels than hobbyists normally work at. You should find that speaker cables are thick and have thicker bundles of strands which are harder to solder than normal line level or guitar level cables. A lot of times, a normal soldering iron isn't enough to effectively solder large wires and to larger lugs. I had to get a higher powered solder gun with a larger tip than a normal electronics iron in order to effectively solder speaker connections.
The risk of bad soldering in this project extends all the way to possible damage of your amps. If something shorts or a solder joint goes cold, you could overload or unload the amp and that can put damaging stress on the output transformer. I recommend you consider the fact that you had to ask for advice on this project as a signal that you might not be ready to DIY something that could damage some nice amps that you are "proud" to own.
Option 1: Two jacks, one 16 Ohm, one 4 Ohm
This is theoretically possible but unlikely to work in practice. I was able to draw up a wiring diagram where the wiring is automatically switched based on which jack you plug into (lower left corner of the image). In order to do that, I had to draw it with two 1/4" TRS jacks that had both tip and ring switched. So great, right? The problem is in practice I've never seen switched TRS jacks that are built for speaker level signals. They may be out there, but it might be a pain to find them. I think one reason why they probably don't exist is that the contact surfaced inside the jacks for switching purposes are just too small to handle the kind of current you want to be ready for in a speaker cabinet.
Option 2: One jack with a switch that changes from 16 Ohm to 4 Ohm
I think this is the way you'll want to go, assuming you can find a high current DPDT switch (pretty sure DPDT is enough). If you look at the lower right hand diagram in the image below, that's my suggestion for wiring up an impedance changing switch.
The + and - shapes on the right side represent the positive and negative terminals of each speaker. Obviously the polarity of the speakers is critical for this project, so make sure you know which is + and which is - for each speaker.
Make sure you get a DPDT switch that has large enough lugs to handle the speaker cabling (I hope and expect they exist), and look for ones that have a rated power or current capacity that is sufficient. Also you might look at a rotary style DPTP switch, since that way you can use the existing hole in the connection plate of the cabinet. Just remove one of the speaker jacks and put the switch in its place. Use an office label maker to label the switch positions.
Below I've shown my whole thought process, so you can do this kind of thing for yourself next time, perhaps. When I'm trying to figure out a switch, the first thing I do is draw the two states I want to switch between without the switch. Then I try drawing the switch using the two states for reference.
The first thing to look for is what doesn't change between the two states. In this case, the positive terminal of one speaker is always wired to the tip of the jack, and the negative terminal of the other speaker is always wired to the sleeve. So with the switched diagram, the first thing I do is draw those connections, since the switch won't change them.
Then I assume the switch is in one position and try to draw that out. Then I try to draw the other position without changing the wiring for the first position. Sometimes I have to do a couple revisions. At this point I'm pretty good at DPDT switches so I can get it on the first try most of the time.