First, battery-powered chainsaws produce very little noise compared to their gas-powered counterparts. This is important because it means you can communicate with your man on the ground without turning off the chainsaw. That also means you don't need to pull-start it again while at height.
Second, battery-powered chainsaws produce no emissions. This is important for two reasons: first, it's better for the environment; and second, it's better for your health. Exposure to gas fumes can be harmful, so using a battery-powered chainsaw eliminates that risk.
Finally, safety features like the handguard on the Swift 40v chainsaw prevent you from touching the chain while its moving, and if the handguard is bumped out of place, the chainsaw automatically shuts off.
So how safe are battery-powered chainsaws? Safer than a big, dead tree branch that could fall through your kid's window. Safety is relative and you always face tradeoffs. You have to cut that branch down, so find the safest way to do it. If you need a chainsaw, then choose a safe and reliable one. Battery-powered is the way to go.