I would never oil the inside. Remember: valve oil is NOT food safe and if you oil the bore, you WILL breathe in the vapor.
Regular maintenance should include bathing the horn in proportion to how often it is played.
Supposedly WD40 is food safe and designed to displace water (WD=Water Displacement). That may be an option, but just as I prefer bathing myself, my horn certainly deserves regular attention too!.
@barliman2001 said in Mute Clarification?:
@j-jericho As I do have a derby mute, but no derby hat, I think I'll settle for the mute...
Playing into a "soft" mute of any kind means that there is enough damping to kill overtones. A normal "hat" or derby mute is OK but putting some additional damping material performs the conversion. Kill the overtones on a trumpet, and it sounds more flute like.