I'm not sure for small breeds since I have a medium/large breed pup, but if he loves wood, the gorilla wood chews have been a hit in my house. They sell them in smaller sizes for smaller dogs, they're not too hard and they last quite a while. They don't splinter, but you do have to monitor as the wood shavings will get everywhere lol and just to make sure he doesn't try to eat any of the larger chunks that fall off.
https://www.amazon.com/Ware-089655-Gorilla-Natural-1Piece/dp/B017D9F70I
When I had my dog he would constantly chew up the baseboards or anything wood and he loves sticks. I was at one of the local pet stores in my area and saw these wood chew blocks and picked one up and he loves it, the only down side is little pieces from him chewing would stick to the carpet but it came up easy with the vacuum.
Ware Manufacturing WARE 089655 Gorilla Chew Natural, Large, 1Piece https://www.amazon.com/dp/B017D9F70I/ref=cm_sw_r_cp_api_GvHtBbTH80MSD
Along with the recommendations of blocking off his access with gates or sprays (sometimes they work and sometimes they don't), I would recommend a wood chew to see if he just really likes the texture of wood. We bought one for our dog when we moved to a townhouse from a house that had a lot of sticks in the backyard and he loved it.
This is the one we have: https://www.amazon.com/089655-Gorilla-Natural-Large-1Piece/dp/B017D9F70I/ref=sr_1_5?ie=UTF8&qid=1517520880&sr=8-5&keywords=wood+dog+chew
It's really hefty and just kind of shaves off because it's a soft wood. Most dogs who've visited us have chewed on it, and it's still surviving a year and a half later!
Are you looking for something totally non-consumable (like a plastic or rubber chew toy) or just something that doesn't add too much to the diet?
We've had a lot of success with long-lasting pressed dairy chews like yak milk "bones" you can find at Petco and similar. When ours was a puppy she also loved lamb and pig ears which are cheap there too -- now we buy bulk packs of cow knee caps (feels weird to just have literal knee caps lying around our house but they keep her busy, I just don't know if they're recommended for puppies).
Our dog also consistently loves these 'gorilla' chews made from manufactured wood (https://www.amazon.com/Ware-089655-Gorilla-Natural-1Piece/dp/B017D9F70I) -- she loves chewing sticks and these are essentially wood, but some sort of texture that doesn't splinter. They get gnawed down verrrryyy slowly so no mess, and if any of this "wood" is ingested it's a miniscule amount at a time and totally safe. She goes back to those over and over and we still have the ones we bought her almost a year ago!
gorilla chews are great :): https://www.amazon.com/Ware-089655-Gorilla-Natural-1Piece/dp/B017D9F70I/ref=sr_1_3?crid=1CJKVV76WGESN&keywords=gorilla+chew&qid=1642464112&sprefix=gorilla%2Caps%2C492&sr=8-3
they last for ages. The wood sort of crumbles so they don't splinter at all.
there are gorilla wood chews (https://www.amazon.com/Ware-089655-Gorilla-Natural-1Piece/dp/B017D9F70I/ref=sr_1_1?dchild=1&keywords=gorilla+wood+chew&qid=1613941652&sr=8-1) if he likes pinecones (i have not tried them, they're just wood). antlers are another suggestion, the marrow may have protein, but you can get a whole antler so they can't really get to the marrow inside.
Are benebones ok? Our pup has those and she doesn't really ingest them, she's been working on the same two from the puppy starter pack since we got her. The soft nylabone she destroyed but maybe the benebones are ok?
It's exactly what it looks like. A log for the dog. It's a chew.