Simon,
Why worry about the extremely minute amount of radiation from small tuner
coils and components when this is hopelessly swamped by radiation from the
nearby antenna, even from the back of a beam, and there's always some
significant amount from the feedline.

Think in terms of relative magnitudes.

The amount of radiation depends only on one dimension, ie., the physical
LENGTH of what may be imagined to be radiating. Imagination is the keyword.

There is hardly any significant difference in radiation from a tuner between
a plastic box, a metal box, and no box at all.

I prefer no box. Stray capacitance is smaller. A metal box behaves as a
shorted-turn around the coils and results in power loss. And it's nice to
be able to see the position of the roller coaster and the tuning capacitors
without the tedium of unscrewing all the screws in the cover.

There may, of course, be a slight advantage of a box, metal or plastic, in a
dusty atmosphere or if you are, like me, a nicotine addict.

Alcohol addicts will automatically ignore this mild advice anyway.
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Reg, G4FGQ