You don't need a battery or wiring to make the engine run, but you need to run the small coil wire to a toggle or kill switch and the other side to ground, so you can ground the coil when you want to turn it off.
I always, check or replace the plug and check for a spark and check the gap around .028" will work for starters. If you have a good spark, you can move on. Make sure all your bolts are tight. If the pull starter works, open the piston with the hole, in the carb, put a teaspoon of gas there or in the plug hole and pull start it to see if it pops or fires and or runs.
You have a 49cc Zenoah piston port copy engine, with a copy carb of a 15mm Walbro WYK pumper carb. Need to push the bulb a few time to get gas from the gas tank, needs a choke when cold. I have all kinds of new parts for that engine, cause I have a seat go-ped style scooter. I put a billet alum manifold with boost bottle fitting amd a WT-813 Walbro w/ acell pump for great starts, designed for your engine, and then a V-stack w/ choke cause the 813 has no choke plate, and a Jet Pro racing exhaust, it wants to pop wheelies & it only weights 48lbs. A Cateye is probably closer to 100lbs. You need an X1-X7 HP Fatty exhaust.