A very commendable ambition.
A couple of observations.....
Whatever about American Spanish being understood or not (not is my experience) even Spanish Spanish can be quite regional. A word in common usage in the north may be less common in the south, for example.
Something like Amazon can be a useful tool for the international bike traveller. Simply put together a component list and you can access that from anywhere, either to order for yourself or to show the guy/gal in a shop. Copy the details in the .co.uk site and search the .es site.
As has been alluded to, the communication issues may be less about the vocabulary but the language around the vocabulary - are you getting a wheel rebuild with new spokes or the old ones? (Personal experience!)
Anything special/unusual/unique about your bike should be well researched in advance. For example, my bike (until recently) used a 7 speed cassette but I have (always) had to argue against the assumption that what I needed was a freewheel, not a cassette. Understanding the difference between the two terms in various languages has been useful!
Finally, as someone who struggles to describe anything beyond the most basic components in English, I'd suggest being careful of overstretching ourselves in a foreign language. Sometimes we just have to find an expert we can trust and let them do what is needed.
Suerte!