Personally I'd use a small LiPo and your favorite dipped ematch (or undipped, for CTI) for sustainer ignition. The Eggtimer won't care... it can pretty much light anything given a big enough battery.
Read the section on airstarts in the manual. Twice. Then again. Then memorize it. For airstarts to work safely and reliably you need to properly set 1) Your CHB setting (breakwire or no breakwire...) , 2) Your CHB "firing time", 3) The LDA, 4) The Burn Timer, 5) The Airstart Delay, and 5) The Minimum Velocity at Airstart setting (if you use it, but highly recommended by TRA). That sounds like a lot, but it's really no different than any other flight computer that will handle airstarts with proper time/velocity controls. Perform a good sim with OR/RocSim, set the Eggtimer to match the sim, and you'll be just fine.