The typical solution to this is not to try to inject commands into the existing remote control encoder, but rather to replace it.
Typically you start by connecting a simple USB-based logic analyzer to the signals feeding the RF submodule that is attached at the top of the board. You can do some initial identification of the lines (almost always an SPI bus, possibly with an additional enable, but very rarely a custom baud rate UART) with the analzyer's GUI interface (or a scope if available). Once you know the electrical format, you identify operations on various registers and figure out which RF chip is being used from comparison to data sheets of the likely suspects (nRF24/Beken, A7105, XN297, etc). Then you write a custom streaming decoder for the packet registers for that to plug into logic analyzer software like sigrok, so that you can move the sticks and see which parts of the transmitted packet change. And you figure out the channel hopping scheme from the writes to the channel registers.
With all of that, you have what you need to make an Arduino-like board run the RF module - or often an alternate sourced one. People have also working out how to make the nRF24L01+ talk to some similar concept chips with notably different on-air format like the X297.
It's quite likely though that you will not have to do this entire task yourself. Typically, the R/C hobby community quickly reverse engineers all of this for any interesting inexpensive toy aircraft, and creates code to the able to operate it from a hobby grade transmitter, either running the "Deviation" firmware or as a plug-in-module which takes legacy multi-channel PPM input and uses an Arduino-like MCU to encode any one of a number of toy protocols. So first do some looking on places like rcgroups for existing work on this particular toy.
In fact, the Deviation project Wiki lists the WL-v262 as using an nRF24L01-compatible radio, with what has come to be called the "V202" protocol, so likely everything you need is already available between that and the more Arduino-ish PPM translator implementation at https://github.com/pascallanger/DIY-Multiprotocol-TX-Module.