DD began with piano but then asked to start a woodwind instrument and, later, a string instrument. We were pleased about this because it meant she could join orchestras with all the social advantages of that.
Otherwise I doubt if we would have made the contacts we did with the local music service and, hence, learned about the junior conservatoire she eventually joined. (We are not musical parents.) Piano can be quite isolating. So you should encourage his desire to learn the oboe for this reason and also because oboists seem to be a bit thin on the ground so he will be very welcome in county orchestra, secondary school orchestra etc.
Another reason is that applicants to junior conservatoires such as Junior RNCM are expected to play two instruments (one can be voice) but the audition is really about how well they play their first study instrument. Playing the piano at the standard he already has achieved is a pretty good assurance of success at audition. Merely showing some promise with the second study should be sufficient.
The fees for junior conservatoire might seem high but, as I said, they have bursary schemes and by the time you add up the cost of private tuition for two or more instruments and music theory, accompanists for exams, sheet music etc etc it means you're not paying out all that much more even without a bursary. (You can borrow music from the college library instead of buying three books for an exam which he'll only need for one piece from each.) It also means you won't have to sit in your car outside a teacher's house for an hour two or three weekday evenings when he gets older.
The beauty of her going to conservatoire for me as a non-musician was that all the advice and guidance she needed was there under one roof and I never again had to search for an accompanist or a teacher or sheet music - or suffer the consequences of a bad choice!
DD also had an absolute ball every Saturday and then stepped into a ready-made social life by joining the orchestra at university.