I'd go up Tuckerman's and down Lion's Head--steep up is easier on the knees than steep down. Both are on the "somewhat" protected east side. (The prevailing winds are from the west, but of course can come from any direction at any specific moment.)
I'd much rather go up Lion Head and down Tuck's. Or just go up and down Tuck's - it's so beautiful that it would absolutely reward the there-and-back trip. Ammo is much rougher on descent than would be Tuckerman - I did Ammo up to the hut and back May 12, a day where the gusts from a couple hundred feet below the hut and above were 70 mph in the 3:30-4:30 pm hour when I was there, with steady winds at 50. That definitely is too windy, and bear in mind the forecast for that day, beforehand, was similar to the forecast the OP now is looking at, so those winds can easily bump up a lot higher than forecast, even if the sky is blue and beautiful, partly cloudy as it was 5/12. (The Mt. Washington Observatory's recordings for the 4 pm hour, iirc, were of steady 70 mph winds with gusts to 86. Windiest day of May, and I reached the hut, as it happened, at the windiest time.
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Ammo is a very tough, rough descent, but doable if you are suffciently well conditioned and take the care and time needed. I did Jewell up and Ammo down, with the A.T. links in between on a nigh-windless day 6/17. That was amazing. Ammo on descent that day, as tired as I was, testing the limits of my strength and stamina, was very difficult and mentally taxing, venturing seriatim a knee or ankle blow-out or broken leg. It was harder than I remembered from the month before, even though dry in June where it had been wet and snowy/icy for the highest 1000 feet or so in May - traction had made a big difference.
Went up Tuckerman and down Lion Head July 22. Tuckerman was steep but very well constructed along the main headwall, and the views were amazing. It was a beautiful climb and would be a very pretty descent, forgiving, relatively speaking, on knees and ankles. Lion Head, at the end of my biggest single day elevation gain, was brutal, especially the mile or so descending from the head of the lion to the Tuckerman trail. Definitely knee blow-out territory, if anything worse than Ammo. Ascending it would be much better - it is quite pretty and would be a fun challenge to scramble up.
My recommendation to the OP, to minimize wind exposure, maximize enjoyment and spare the knees and ankles as best possible? Go up Lion Head and down Tuckerman. Or if that idea makes you a bit anxious, then eliminate the fear of Tuck's by going up it and seeing how relatively easy it is - no kidding - and then go back down it. But given your concern for knees and such, give careful thought to going down Lion Head or Ammo, especially if you don't go up them first. They are doable, but daunting.
Another possibility - go up Ammo, cross over to Tuck's to get wind shielding, then up to W and down via the Cog if the winds are too much. Jewell is, as trail, relatively easy b/c its grades are pretty steady. Footing can be tough above tree-line on it and on the A.T. routing, as others have noted, but the views are spectacular.
Bear in mind that climbing the summit cone above Tuckerman's junction, while breathtakingly pretty, is a strong workout in itself. I found it harder than the headwall, though that probably had something to do with tiring after doing the headwall. The cone was easier on descent than I expected and got much rougher once I took the left turn onto Lion Head Trail, which is easy only for the short stretch from the Alpine Garden junction to the Head and for the brief bits on either end near Tuckerman Ravine Trail. The rest of it is quite rough with little relent.
Whichever way you go, it's beautiful, but approaching from the east is nicer when the west winds are strong, and there's no reason to choose Ammo over Tuck's on account of knees and ankles, in my experience.