I have seen the Messenger of Allah ﷺ using a tooth-stick while he was fasting. Musaddad added in his version: "more often than I could count." (Using translation from Abū Dāʾūd 2364)
رَأَيْتُ رَسُولَ اللهِ ﷺ يَسْتَاكُ مَا لَا أَعُدُّ وَلَا أُحْصِي وَهُوَ صَائِمٌ