Mujitsu and Tairaku's Shakuhachi BBQ

Greetings and salutations everyone.

I am a complete novice to Shakuhachi, and currently have two flutes.

The first is a single piece relatively straight flute made by Noel Dowling, and the second a single piece, root end flute.

Both 1.8, in the key of D (I hope I am getting this right) i.e. approximately 40 cm long.

Noel's flute (lacquered) has the inlaid uteguchi, and the other (possibly much older) has the non-inlaid style of mouth piece.

I am pleased with my progress (beyond my highest hopes already) in that the lowest octave has revealed itself, and I'm starting to make other progress after only a few months.

I am also blessed with a friend who has agreed to teach me, and she has experience of at least one masterclass with Riley Lee.

Would forum members recommend that I treat the older flute with oil, now that it is in my hands?

Since this one has been purchased from ebay, I really don't anything about it's history, or even where it was made.

I have read some of the posts on the forum, and note the reference to tea-tree oil. I also have other oils (e.g. Tung, Camelia) etc. through my wood-working efforts.

All directions to appropriate posts/resources would be gratefully received.

Andy.