There was plenty of harm in waiting. Specifically, there could be small, infant-shaped harm in waiting. Remus knew, rationally, that births took a long time, most of the time, and that it was reasonable for Tonks to wait until she was sure the process was further along before doing anything about.
But reason did not help him to stop he visions of tiny babies plopping out onto the floor.
But still. He wasn't panicking. Or wouldn't admit it. "You're sure you can apparate like this? It won't. . . interfere? Or speed up?" To cause the spontaneous birthing. It took a little more prompting on Tonks' part, but Remus finally did wrap his arm carefully around here, and then take them both back to her new flat, waiting for the dizziness of apparating with someone else to fade and then starting to guide her toward the bedroom. Without asking. She was IN LABOR. She should be lying down!