IMHO
For - - > Clean (not deeply stained) Raw Teak and Mahogany... Interior or Exterior: Nothing beats two to four thorough coats of pure Baby Oil well rubbed in with a soft towel, let set for about 15 minutes between coats as it soaks in, then vigorously polish to a sheen with a clean, soft cloth!! Interior lasts for two years or more, exterior for one year or less (depending on climate).
For - - > Clean Varnished Surface (with the varnish finish in not too bad a condition): Diluted laundry detergent, 1 cup +/- to 4 gal water – gently hand wash with fluffy towel. Dry and hand polish to a basic gloss with car shine type of buffing pad. If still dull - bite the bullet, i.e. sand lightly with medium to fine grit and varnish with number of coats required, very fine grit sanding between coats and wipe down with damp towel to remove dust (let it well dry between coats).
How do I know... Teen years (and before - lol) restoring wood cruisers in NY boatyards, with the pros! I still do these processes today!
Pict - Draws and doors in galley are teak.