It would normally be considered an error to say:
"I can enjoy my travel without...."
This doesn't mean that native speakers never use such constructions (everyone makes mistakes) but (1) they are rare, normally one would say "enjoy my journey" or "enjoy my holiday", and (2) You would be judged by other native speakers.
Now you may not care what other people think and that's okay; many native speakers don't care much. But if you are trying to speak correctly, you should avoid this construction.
It might be worth noting that it is quite common to use "travel" as a noun adjunct in expressions like "enjoy my travel writing" or "enjoy my travel blog".
Thus "travel" is a defective noun. It has countable and uncountable senses, but the countable sense (meaning a series of journies) is only used in the plural. The uncountable sense can't usually be determined with words like "my" or the.