Can I identify an LED's characteristics from the transistor used as its current limiter?
Usually NOT.

That said: there is usually significant latitude when swapping one LED for another that has vaguely similar characteristics.  Most LEDs are supplied with a voltage source that is significantly higher than the LED forward voltage.  Changing the LED to a different color or package will most likely work just fine because a small change in the forward voltage won't affect the LED current noticeably.

Usually, that is.

The easiest way to tackle this project is to just do it and observe the results.