In practice, IR will not work well for a remote-controller aircraft outside, it relies on ceiling reflection to be usable indoors.
If building something from scratch, using a BLE Radio/MCU IC like an nRF51822 in a non-BLE 2.4 GHz mode (ie, nRF24 compatibility) could be very compact. Or use it in BLE mode and use your phone. Note there already is a product for powering/controlling "paper airplanes" that is BLE based. Especially if you use BLE you should make the system cut off the motor on loss of "connection" - and having it cut off after a second or two with no packet getting through at all (losing many packets is normal) would not be a bad idea for any radio mode anyway.
If trying to buy something, just gutting a tiny quadrotor drone for the board is likely going to be your best bet at around 2 grams and perhaps $12 including the transmitter and four little motors. Be very careful not to short out or mishandle the lithium battery. There are alternate firmwares out there for those based on STM32, GigaDevice and Nuvoton MCUs with separate radios, or your could do something like parallel all the motor drivers to largely defeat the control algorithm. Though you might still get some surging if it thinks it's tumbling. A little add-on circuitry could probably interpret any PWM motor pulses from the board at all as a command for full power, and their lack off - but reprogramming the MCU is most flexible and not particularly hard if familiar with MCU programming in general and prepared to solder at the scale of ultralight model aircraft (the SWD pins are essentially always broken out, and sometimes even on a labelled connector footprint).