Deep Space Nine had the Defiant make the trip from Earth to Bajor in somewhere between 3-5 days going by the given stardates between the episodes "Past Tense" and "Life Support".Hmm, so i "learned" a lot looking into this.
Bajor might be 60 or so lightyears from "the core Federation worlds" or it might be 200 or so, depending on the various canon sources used.
Deep Space Nine has an episode where they have to use a shuttlepod with known warp capability to go down to a planet specifically because the shuttlepod doesn't use anti-matter.TNG and later shuttlecraft (and DIS too, due to frankly retconning), did have warp capacity. But I don't think it is clearly answered in canon whether their warp capability was powered by fusion or M/AM reaction. The few explicit mentions of their warp capability describe the millicochrane rating of the nacells, and fandom seems to have concluded that small M/AM reactors are present in the nacelles, walls, or floors of the shuttles.
However, if shuttles could rely only on fusion power, and could maintain warp 5 (TNG scale) for several months (or could change shuttles at multiple stops), and Bajor was only 60 lightyears away, then Ake could have made the trip in about 3 months. So possible, a stretch, but possible.
Also, I'd point out that Deep Space Nine itself was able to travel at Warp using it's fusion reactors when it moved from orbiting Bajor to the Denoris belt.