It is probably easiest to start out assuming certain data formats (async, 1200bps, 8databits 1 startbit one stopbit) and see if it fits. Then try inverted async. Don't forget that this is a cheap consumer product that probably contains a standard microprocessor of some kind, and it probably uses a data format supported by that micro, which is probably an async uart (I2C and SPI being fundamentally more-than-one-wire protocols.)
Can you take apart the existing receiver (or transmitter, except that would be more dangerous) and see what's there? It may have a little 433MHz module just like we use, in which case you can look at where it's being fed from/to.
You can use your arduino as a sort of one-wire logic analyzer for things like this. Sample the incoming bitstream from the receiver module every 10 microseconds or so for the entire duration of the transmission, store the results in RAM and dump to a PC for display and interpretation. Or measure intervals between changes and send those...