He would most likely have to expose himself to Starfleet so as to have the proper equipment to do these things. Even then they would effect the JJverse and drive it further away from the TOS/TNG timeline.
For example intercepting the Botany Bay and leaving it on a planet for its crew to awaken could leave Kirk an Admiral, a job he's not suited for. That would effect the events of UC since Kirk would be an old Admiral who has been out of space to long for the Klingons to think twice about attacking. It would have an even greater impact on TSfS & TVH. Kirk never gets attacked by a vengeful Khan, no fight in the Mutara Nebula, no death of Spock, no defying of orders to return to the Genesis planet to retrieve Spock and reunite his body with his katra. No defied orders, no Court Martial, no demotion to Captain.
As I understood it, the rebooting and the creation of an alternate time line was to allow the characters to have new and different experiences and allow them to grow in new directions. Spock shows genuine affection for Uhura, Kirk presumably was never on the Republic, his chance to learn duty over friendship would need to be learned another way.
Meeting or intercepting the Whale Probe would not be wise, getting Humpbacks from the past and bringing them to Earth to await the probe is the better option. Whiles he's at it he could bring back a breeding population in case the WP decides to drop by again.
