Well, there are so many factors that it is really impossible to give you assurance. I have seen strong 16 year-olds that couldn't make it and I met a couple from Japan at the top and they were 75 years old and celebrating a wedding anniversary. They didn't look as tired as I did and I was 30 years younger than they were at the time.
In many ways the hike, except for the distance, is too many people much easier than the much steeper hike to the top of Yosemite Falls. On Half Dome you are gaining, on average, about 500 feet per mile in distance. The Yosemite Falls hike is about 1000 feet per mile and really more than that because the second mile from Columbia Point to the middle falls is relatively flat. So you might say you are going up 1500 feet per mile in the two miles that are not flat. I think the Yosemite Falls trail is much steeper overall and I have friends who would rather do Half Dome.
That said, you are still talking about 17 miles roundtrip to the top of Half Dome and on a hot day it can be long and tiring. Our group usually goes up the John Muir Trail where it splits off from the Mist Trail and we come down the Mist Trail from Nevada Falls. The two trails meet near the top of Nevada Falls. You can get wet early in the morning going up the Mist Trail and that's not much fun if it's chilly in the morning, plus there is a very steep section as you go up the side of Vernal Falls. So we go up the JMT and come down the Mist Trail later in the day when a cold spray from Vernal Falls feels good. Before I forget, the first 3.5 miles to Nevada Falls is relatively steep, then you get a nice rest for your lungs, knees, and ankles for about a mile as you go through Little Yosemite Valley. From the end of that, you have another 3.5 or so to the top of Half Dome.
THE CABLES....first of all they can look intimidating ezpecially if you have a fear of heights. I've seen many people make it easily to the bottom of the cables and decide to go back. But if you've gone that far you have to go for the top. It's truly not dangerous to any extent going up and even coming down no one has ever been killed by falling off the cables. Not one person in all the years the cables have been up. A few have been killed by lightning because the cables are steel and you are at a very high, exposed sight. They warn you if you see any sign of lightning in the area don't go near the cables.
But assuming a sunny day, you have 800 feet of steel cables to go up. You have a cable on each side of you that is threaded through steel posts all the way to the top. Approximately every 20 feet, or so, there are wooden 2x4s between the posts where you can brace your feet and rest. If people are coming down while you are going up, it's good to hang on to one side of the cables and let them pass. They will be going much faster than you since gravity is working for them. By the way, the cable can be frayed in places, so be advised to wear gloves to protect your hands while going up and down. People leave gloves at the bottom of the cables, but they can be pretty cruddy, so best to bring your own. A nice leather pair will hold you better than a cotton pair. I try to break the trip to the top into about eight 100 feet stretches. A lot of people never stop at all, but my lungs aren't what they used to be. You mentioned upper arm strength and that shouldn't be a problem. I have a friend whose wife weighs less than 95 pounds at about 5 feet tall and she makes it to the top without any problem. In fact, she usally beats us to the top and we tell her that's because we are pulling up a lot more weight.
The method for coming down varies by person. I like to come down like you are coming down a ladder -- in other words looking up instead of looking down. You can somewhat feed yourself down the cables resting on the 2x4s. But many people like to go down facing down the granite. I don't like that only because if you slip it would be harder to catch yourself if you are facing forward. But you will see both methods of going down the cables.
Sorry for the long post. I may have confused you more than helped. I don't know if anyone -- even if they knew you -- could give you total assurance. Heck, I didn't know myself if I could make it the first time. But I did and I've been to the top over a dozen more times since. Each time I seem to enjoy it more. It's not scaling Everest, but it is a great hike and I can't wait to do it again.
I should have also mentioned that it's best to start as early as you can. You want to get to the cables early, because it gets very hot up on the granite between 1-4pm on most summer days.
After you get safely back, you will sleep like a baby that night. And the next morning you will get out of bed hurting in places you didn't know you had. But it's a "good" hurt, if you know what I mean.
Even for those who choose not to go up the cables, it's still a great hike.
Be safe and good luck.
My lawyer requires me to say that the above is not a recommendation to go for the top and the end user assumes all risks if he/she decides to do so. But if it was me going to the top of Half Dome, I would:
Start early- maybe 6:00 a.m.
Take suffcient water, food, and first aid.
Go up the John Muir Trail and come down the Mist Trail.
Get to the cables by 11:00 a.m.
Spend an hour at the top enjoying the perfect view.
Glide back down and start to plan my next return hike to the top.
Bill