What type of product can I use to hang wall art on bare wood that won't damage the wall?
Two approaches come to mind:

Thin nail picture hooks



These use very sharp, very thin hardened nails that can be removed leaving a hole so small it is nearly invisible, even in finished wood. If it were noticeable, it could be concealed with touch up wax. Various weight load sizes are available. The sizes that have the thinnest nails can hold at least 20 lbs. each, more if pairs of hooks are used.

Removable hooks



These are glue on devices in which the glue strip can be pulled to remove, supposedly doing no harm to the finish of the wall.  These hangers are limited to loads no greater than 5 lbs., but the use of two hangers would increase that load.

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