Two ideas:
1. use ready to buy equipment (muxer) with 10A! switching capability (SCXI??) that you can easily control with LabVIEW
2. (ab)use ONE RS232 hardware handshake line (DTR) to control 4 opto mosfets (solid state relay with optocoupler)
DTR line state can be accessed by VISA proberty node. DTR to GRND will be +/-10-12V(or so)
(not with a Laptop, use USB/Serial) and can drive some mA (enough for two LED in serie).
Connect two optos serial and the two pairs antiparallel. like that always only two of them are active.
As a current limiter for the LEDs one Resistor should be added (range depends on current of optos)
Or use a standard optocoupler and external power to drive a commercial pole changing relay
However additional protection circuitry should be added to protect whatever relay or switch if you want to or have the possibility to (e.g. always) change the current in a inductor. (You mentioned a current sweep, so you already plan to switch the leads at I = 0 A, but you never know)
Greetings from Germany
Henrik
LV since v3.1
“ground” is a convenient fantasy
'˙˙˙˙uıɐƃɐ lɐıp puɐ °06 ǝuoɥd ɹnoʎ uɹnʇ ǝsɐǝld 'ʎɹɐuıƃɐɯı sı pǝlɐıp ǝʌɐɥ noʎ ɹǝqɯnu ǝɥʇ'