kitrob, last summer I did a custom trek to K2 and G1 and G2 base camps, including a camp at the base of trango towers. I think you should be able to do such a trek at age 62. Many of the treks just go to Concordia. On the rest day of Concordia, some groups trek to K2 base camp and back. There just weren't many trekkers is this area last year, and the few that I saw, most were younger. However, I have done a lot of trekking in Nepal, and I have seen many trekkers in their 60's and 70's and they do just fine. I am in my 50's.
On the trek, we usually left camp around 8am, stopping around an hour to an hour and a half for lunch, and then pulling into camp at 3 or 4 pm. If you were slower, and you arrived at camp an hour later, I don't see it as a big deal.
I would look at booking a custom trek, with perhaps shorter days, since you are concerned about your age. Then, the trekking agency could offer it to others. They would just have to understand that its a trek made for older individuals as opposed to trekkers in their 20's.
If this is a trek that you want to do, I'd encourage you to do it. The mountains are incredible! I hope to be trekking into my 70's.