The answer is yes, and it does not take more than basic carpentry skills to accomplish. But be aware of a couple of things.

First, the kind of hoods you are talking about often have internally mounted lighting fixtures which use halogen or incandescent/CFL bulbs. These produce a lot of heat. To dissipate the heat, there should be be a small louver/vent on the top side of the hood above each fixture. I have seen a several less-expensive of hoods without this venting. the idea apparently being that the metal is thin enough and the internal space large enough to provide sufficient dissipation of the heat from the bulbs. If you get one of the hoods with the topside venting/louvers, you want to design your cladding with cutouts and some kind of grill. (Heavy screening material would work but might look funky. Maybe you could find some brass grill at a fireplace or hardware store. You want to be sure any topside louvers/vents are not blocked with the insulation or the wood claddding. Avoid buying any of the really thin (5 or 6 inches high) hoods that have internal lights without topside venting UNLESS the hood is designed with LED lighting rather than halogen or incandescent/CFL. (LEDs produce much less heat.)

Second, many "hoods" of the kind considering are designed with flat bottoms -- which is to say that they are venting devices but not actually hoods. That does not keep them from working pretty well, but it does mean that you will have exposed wood cladding right at the edges. Or, if you decide to mount the hood a little high, you could have the cladding extend down to give an actual hood. Either way, you need to be sure to seal the edges of wood cladding. Do not depend on a coat or two of inexpensive paint or varnish. Get (or have your contractor use) sealers or paint that can take some heat and the moisture/steam-condensate.

As I submitted the reply, I remembered something else from my hood-and-cabinetry remodel a few months ago. Are you planning for a hood and chimney against a wall without overhead cabinets? Is your hood going to vent out through the roof or go up near the ceiling? If so, you might consider skipping the cladding of the hood and just box the chimney with drywall. It will look like the kind of chimneys that were common for the coal and woodstoves that were common a century ago. (Around here, these are referred to as "half-chimneys" meaning that they come about half-way down from the ceiling and fair-back into the wall). I considered doing that design but decided that I wanted more cabinets and was also able to vent out the back wall rather than needing to go up. But, if you are not going to have cabinets there, the idea might work for you.

Please disregard this idea if you are doing an island hood.

The folks over at younghouselove did this, although their work methods usually involve reinventing the wheel at least two or three times during the course of any project. (They don't seem to realize that people have done work for centuries and know how to use the right tools for a job.) But it did work out for them.

However, it did seem to me it would have been both easier and cheaper to build a box for regular hood liner insert.

Here is a link that might be useful: younghouselove hood project

Forgot to say that liner inserts are more widely available these days and not so expensive. Even our Lowes has them for the same price as the lower end hoods.

Liners are not expensive at all and are designed from the beginning to accept wood. I'm talking around $300 for something basic to start. It will all dependon the CFMs you need to achieve as well as how easy you want it to be to clean.

If you proceed down your current path, you need to be sure the mounting brackets of any metal hood you are dealing with are sturdy enough to accept the extra weight as well as the hood itself being wider and deeper than the cooktop below it. You do not want any of the wood to be directly above the cooking surface. That is a fire and safety code violation.