First thing I would do is turn off the console.
take out the SD card to update
Hekate first. Just grab the latest version and drag and drop the bootloader folder onto the system's SD card. The .bin payload that is included is used with your RCM loader to start hekate while the system is in RCM mode.
After you get hekate updated you can do the same for
Atmosphere and your Sigpatches. Just download the latest and drag and drop.
Since you don't have a jig handy I would suggest getting the system into RCM using a more annoying method such as a paperclip and then just enabling autoRCM.