I am a Very seasoned Woodworker/furniture maker. You want to stay away from woods with a lot of acids in it. Look up wood toxicity levels of different species. Stay away from walnut, oak, wenge, bubinga, zebra wood and Iroko and oily stuff like teak or some mahoganies like Santos. The best shavings I found are the best for bedding is stuff from a molder of shaper(router table). Carvings, lathe shavings minus the fine dust is ok But be careful of the long stuff, It may create injury. You could use the sanding dust and maybe fire pit ash and some sand in a kiddie pool for a dust bath. But yes use the saw dust for the compost, Especially when you nitrate (stanky too wet material) level is up. If it is too dry add lawn mowing clippings to it. Never put animal fats in compost, keeps away mice and aromas. (if you didn't know already.lol)