Sure, I've a few thoughts
1st thing to understand is, your technically strengthening your thighs, your knees of their own have no strength (simple joint). So, we need to concentrate on working the thigh muscles.
The easiest exercises do not require any special equipment. Have you a good set of stairs? Start by going up and down a few times, and after a week or so, try two steps at a time.Later on carry some weight as you climb. Take your time advancing to weight, that will be at least a few weeks...DO NOT overdo this stuff..Go easy and slow at first.drink plenty of water too..
Knee bends- Stand with your feet at the same distance apart as your shoulders (just a little apart) and squat down slowly, and return to upright.
You would start easy at first, do 5-10 knee bends, take a few minutes, and return to it. Maybe 3X at first, every other day, and after 1 week, maybe a week and a half, Increase the squats to 15-20, 3X, every other day.
There are many many ways to easily strengthen your lower extremities, I do them 4X a week myself, Including squats w/dead weights. I woudn't think you'd need to worry about weights at this point.
One more thing, be sure your Physician knows and is OK with your exercise program, and BE SURE TO STRETCH before and after your exercises.
Toe touching a few times is a good start, but DO NOT over-stretch your limits, don't force yourself down too hard or fast.
Best of luck.... -Lw