Finishing Teak...

looks good, i would go with the teak oil.

I would get a marine-grade exterior polyurethane (what is used on all the teak spearguns). It'll seal out 100% of the water. You may run into trouble getting a good coat inside the "barrel" of the handle.... If you can't get a good coat insided the barrel the "edges" where the polyurethane stops will be weak spots in the seal. So if you can't get the inside done well you're probably best off going with riffehunter's suggestion and use an oil. Nice looking handle by the way. Most of my DIY stuff looks terrible so it's always nice to see that it is possible to produce quality work.

Teak has its own high oil content which is one of its great advantages but also one of its biggest disadvantages. It is resistant to penetrating finishes no matter what people tell you, oh yes it will absorb a little into the pores but a hell of a lot less that say Oak.

Linseed oil is a non drying oil so will tend to remain sticky on the surface - not nice

Teak oil is a drying oil and can be used but will require the wood wetting and cutting back the raised fibres a few times first.

Tung oil, slower drying than Teak oil but a durable finish

Diluted epoxy, if mixed very thin will over 2 or 3 coats provide a good level of protection. Use varnish on top of this to provide protection against UV light

Un treated, due to its high oil content and the fact that it will be allowed to dry out after use teak would be fine un treated, just wet and cut the raised fibres back a few times to keep it feeling smooth. It might go a little grey looking but that is OK, all the above will do is keep it looking brown at the end of the day

Hit it with a heat blower, submerse it in teak oil for a day, let it drip dry...then go bloody it up...nice work BTW