If you plan to use the bottle within the next 5 years or so, there's nothing to worry. Just make sure you don't tilt the bottle.
Contact with oxygen will over several decades affect the quality of the perfume, but we're talking about decades. Oxygen is present in all bottles, also those that have seals. If the bottle leaks, then there's just a little bit more oxygen contact - but this is marginal. As you are doing, light and temperature are more important factors.