It would be very difficult to wirewrap a board that could support a 486, starting with the fact that I'm not sure wire-wrap sockets exist for it, so you'd either need a breakout or to get one custom-machined.
Once you have that, you'd want to think about clocking the chip way under its typical speed and seeing if it still gives useful results, because birds' nest wirewrap is not going to be especially useful at 16mhz.
You're right that most of the 168 pins in a typical 486 socket are not necessary or are redundant. At minimum you would need power, some address pins (probably not all of them, if you're only looking to run the most minimal program, call it 16 for a two-byte 64k address space), some data pins (again, you can probably get by with 8 if you're willing to use the 8-bit instructions only). There are a few misc pins that I don't know the exact use of, but you'll probably need 4-5 to do things like understand when the bus is in use, set up 8 bit bus mode etc.
Then you can think about what kind of i/o you want. For a minimal project, you can probably get by with driving LEDs straight from from address pins (i.e. read from a certain address in a tight loop to light it).
From here you can blow some ROMs with simple programs and convince yourself it works, but at this point you're really just treating a 486 like a 70s era micro (8080, 6502, CDP1802, etc) in a "trainer" like the KIM-1 (http://www.6502.org/trainers/buildkim/kim.htm).
Once you have that, you'd want to think about clocking the chip way under its typical speed and seeing if it still gives useful results, because birds' nest wirewrap is not going to be especially useful at 16mhz.
You're right that most of the 168 pins in a typical 486 socket are not necessary or are redundant. At minimum you would need power, some address pins (probably not all of them, if you're only looking to run the most minimal program, call it 16 for a two-byte 64k address space), some data pins (again, you can probably get by with 8 if you're willing to use the 8-bit instructions only). There are a few misc pins that I don't know the exact use of, but you'll probably need 4-5 to do things like understand when the bus is in use, set up 8 bit bus mode etc.
Then you can think about what kind of i/o you want. For a minimal project, you can probably get by with driving LEDs straight from from address pins (i.e. read from a certain address in a tight loop to light it).
From here you can blow some ROMs with simple programs and convince yourself it works, but at this point you're really just treating a 486 like a 70s era micro (8080, 6502, CDP1802, etc) in a "trainer" like the KIM-1 (http://www.6502.org/trainers/buildkim/kim.htm).