Mesa Arch is reached on foot over distance of less than 1/2 mile. The path is paved part of the way and rises for perhaps an eigth of a mile and then drops. The last 1/8 th mile continues dropping, unpaved over moderate rocky terrain. Perhaps your father could do this in daylight but I would not suggest taking him there before sunrise. It is a great spot but I consider it unsuitable for your father, way too risky in the dark.
You also have to consider how far this location is from medical services. It's a good 45 mins one way from Moab, not to mention limited cellular service in the area. A fall or twisted ankle could require a long wait for assistance. (I'm sure the NPS and/or the Utah State park folks just across the mesa at Dead Horse Point would be the first responders to an accident in this location.
Sure, the hike to Mesa Arch might not be easy for an elderly person, but there is a reason it's such a popular spot to photograph. The morning light illuminating the arch is just beautiful. I think if someone is going to be in the area (Canyonlands), the sunrise at Mesa Arch is something to see. So, if dad wants to sleep-in one morning, join the crowd at Mesa Arch.
You also have to factor in the Junk Show that is Sunrise at Mesa Arch. I'm not sure that any photograph is worth the rudeness and professionalism that can go on there at any given sunrise.
Here's a hint. There are some really nice vistas in the same area that require just a little bit more work to get to. I would contact one of the major photo guide companies in the area and inquire about one of their sunrise guided tours and what your limitations are. They very well might suggest Dead Horse Point, and I think that makes an excellent choice. But just know there are other less photographed and equally spectacular options in the neighborhood. Best suggestions for photography given your mobility limitations are one of the main vistas like Grandview point or Green River Overlook. There's alot of information online and in books about both of these locations.
Now, with regards to Arches, there are a couple of sunrise options. Usually, I tell first time visitors to hit up the Windows Section for sunrise, but given your fathers age, I'm not 100% sure that's the right advice. While listed as easy in the park guides, trail is likely more difficult than the trail to mesa arch as it has has more elevation gain/loss than the mesa arch trail. They are within a few hundred feet of being the same length. The easiest trail, but the longest is devils garden to landscape arch, it's mostly flat, and very well maintained. But it would be close to a 1 mile in length.
Sunset in arches is easy and likely your best bet. Balanced rock should be at the top of your hit list. Again given your limitations it provides the best mix of scenic value and ease of access.
For midday photography, there are many rock art sites along the Colorado River off Utah 279. Go to the visitors center down town and they have pamphlets with the locations listed.
For MV, if you're going to do it, book a room in the lodge (expensive as it might be) and take advantage of the after dark access.
Well, this should get you started. Have fun, stay safe and post your pics when you return.
Edit: I agree with the sentiment on Dead Horse Point. Very easy access and beautiful vistas.
L