As one of the first two people to ascend all VT6ers in a day, I concur. I would add that you—and any other tempted souls—please be mindful of the alpine flora on the Nose, especially with your dogs. Use a leash if necessary. The Nose was all but stripped bare prior to the closing of the trails to it, and since the closing, the alpine flora has made a remarkable recovery.
Having red-lined the current trail system on Mansfield and all known former trails, with the exception of the Notch section of the Bear Pond Trail and a short segment of the Triangle Trail, and for years ascended it on a weekly basis, I am confident in making my recommendations.
If you're looking for a quick up-and-down, then up Laura Cowles, down Sunset Ridge is definitely the best option, though there are a couple of very brief scrambly moves on the upper part of Laura Cowles. Given its steepness, I do not recommend descending Laura Cowles.
Mansfield has a number of gems and the best trails on the mountain do not go to the summit. If you have to summit, I would recommend the following:
Park at Underhill State Park, take the Eagle Trail>CCC road to the Maple Ridge Trail and ascend to the Forehead. (The upper 0.2 miles is actually part of the Wampahoofus Trail.) From the Forehead take the Long Trail to the Chin, making a side-trip to the Nose. Descend via Sunset Ridge. Without the side-trip to the Nose, CalTopo puts the length at 8.6 miles.
@sierra, I'm going to PM you some extra info. I'm not fan of ascending Sunset Ridge, so if you wanted to reverse the aforementioned loop, I would ascend via the Laura Cowles and descend via Maple Ridge. If you do that, be sure not to miss the right turn back to the CCC road.
Up the LT and down via the LT South>Toll Road>Haselton Trail would be fine for you and your dogs, but it is a much less interesting route. If you did do this route, a side trip to the Adam's Apple is well worth it. The view of the summit from the AA is pretty cool.
The Cliff Trail on the East side of the summit ridge and the Subway system on the West side are marvelous, but not dog-friendly, due to ladders, crevices, ropes, et cetera. The Teardrop Ski Trail is shown on some maps, but it is not designed or maintained as a hiking trail, so I would not recommend it.