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.