That's what I did...let it dissolve.
This has nothing to do with splinters but with more serious things like poisonous spider bites. Years ago my wife was bitten on the back of her neck by some kind of spider, probably a Brown Recluse. At first we didn't think it was any big deal. We were always getting bit or cut or stabbed by something, but after a couple of days it began swell and turn necrotic. And I was able to see the actual bite marks. We went to the ER and they had no idea what it was but said surgery was needed and that it would leave a large depression and scar on her neck. She declined their help. I knew an old timer who had lived in rural Texas all of his life and AFAIK had never been to a doctor in his life. I asked him what to do and here is what he said. He said to make a poultice of hot water and keep it on the wound until it softened somewhat and then to make a slurry out of Garrett Snuff. For those of you who don't know what this is, it is a strong type of tobacco that one either snorts up is nose or dips it. It is a fine powder. He said to put this over the wound and to keep a hot compress over it. He said to keep up the snuff and hot compress until it drained the wound. And drain the wound it did. It took about 12 hours but it removed what I call a core of tissue about the size of a walnut. He then said to wash out the opening with hydrogen peroxide and cover it up. To make this story short it worked, the hole in her neck closed up and she now has only a tiny scar you can barely see.