Can anyone tell me ... can I trigger a Godox SK400 strobe with a Yongnuo trigger/ transmitter? I use a Yongnuo speedlight and transmitter but I am about to buy a Godox SK400 strobe and would like make sure that I can use the transmitter / trigger with both.
The only way you could trigger the Godox SK400 with your current setup would be to use it in "dumb" slave mode where the flash from the Yongnuo speedlight would trigger it.
The radio in your Yongnuo trigger (regardless of which Yongnuo system you have - there are at least three separate Yongnuo radio protocols that are not compatible with each other: YN622, RF603/RF605/YN560, and RT) will neither control nor trigger a Godox SK400 without additional equipment. For control as well as triggering you need either the Godox FT-16 transmitter and the FT-16 receiver module that plugs into the remote port on the SK400 or a Godox X1T transmitter (linked is the Nikon version, but it is also available in Canon and Sony versions) and an XTR-16 receiver plugged into the SK400.
You could use an additional Yongnuo receiver (that uses the same protocol as your current Yongnuo transmitter) with a wired sync output to fire the SK400 via the 3.5mm sync port. Of course you would also need to purchase a cable that fits your Yongnuo receiver on one end and the 3.5mm port on the SK400 on the other end, and you'd only be able to tell the flash to fire via wireless radio. All settings would still require physically making them on the SK400's controls. But I doubt fire only is what you are looking for. If fire only is sufficient then the use of an additional receiver plus sync cord gains you very little compared to just triggering via optical slave mode.
Yes, you can use Yongnuo (or nearly any RF-based) triggers to fire the Godox SK400, since it has a 1/8" (3.5mm) miniplug sync port. You simply have to cable an additional Yongnuo receiver in the triggering system you're using (e.g., YN-622 or RF-605) to the strobe's sync port (this may require a 2.5mm→3.5mm adapter), and the Yongnuo transmitter on your camera's hotshoe will fire the strobe remotely.
Bear in mind, however, that this will be "manual-only" triggering. All you can tell the strobe to do is fire in sync. Nothing else. Depending on the duration of the pulse, you may be able to use the tailsync capabilities of the YN-622 to go past your max. sync speed, but I wouldn't count on it.
If you want to have remote control from the camera of the power over both the flash and the SK400 strobe, however, you'd probably be better off to dump the Yongnuo gear, and move to the Godox X1 system (rebranded as Flashpoint R2/R1 by Adorama). This lets you mix both manual and TTL speedlights, barebulb flashes, and studio strobes, with remote power control, HSS, and (if the flash performs it) TTL.
The XTR-16 receiver can plug into the SK400, and be controlled from an X1T/Xpro transmitter. But power control might be wonky, given that the SK400 does not do ratio power control, and the X1T does not do the percentage power control the older Godox studio strobes do. It would be better to exchange your SK400 for a Godox SK400II, which has a Godox X receiver built-in and ratio power control, so it's fully compatible with the Godox X system.