The logistics of this are a bit on the non-sequitur side, much like the inane dialogue in the DSC pilot episode: we get cool introductions, but they make no real sense in-universe.
Where is Tom coming from? More importantly, where is he going? Not to Voyager, since he's next seen stationside, and is yet to report to the ship at that time. So, did Stadi fetch him from a location other than the ship or the station? A starship that was not docked to the station, and had no interest in docking (plenty of those are seen hovering in the background in the later episodes)? Unlikely - Tom could have simply beamed over, then. More probably, Stadi would have been fetching Paris all the way from Bajor, a doable trip for a shuttle.
Alternately, Paris has already arrived at DS9, and is getting a pure sightseeing tour. But Stadi sounds like the last person interested in giving one to him. That is, she's eager to rattle off the specs of her ship, perhaps to a fellow helm officer even, but she appears to be making an exception in case of Tom...
Where did Harry come from? If from Bajor, why not share a ride with Tom? It's not as if Tom were being hauled around in secrecy, or in chains and under guard.
How many ships fly from Earth to DS9 per week, at that time and age? Would it be reasonable for our two heroes to take different ships? Kim could of course be coming from some other point of origin altogether, but we'd then lose the "really fresh out of the Academy" angle to his character. So perhaps Harry just arrived on the E-D, which chose not to dock because of the congestion caused by Janeway's ride, and this is where the other shuttle came from... (We'd then certainly expect a Janeway vs. Picard kowtow where issues of high moral standards are being discussed over a shared cup of tea or coffee, with Sisko left seething outside for his lack of a proper starship!)
Timo Saloniemi