Hi there! I am so glad that you went to the specialist and got the OK to do SOME kind of squats and lunges. I believe the doctor said you still had a bit of cartilage right? Yes I think you can get results doing modified squats although maybe not as much as doing deeper squats. When evaluating an exercise though you have to think benefit VS risk. In your case, the risk of deeper squats would outweigh any benefit that can be derived. I would make the following recommendations:
FOCUS ON FORM--when doing squats, focus on placing your weight into you glutes and heels and avoid pressing your weight forward to minimize the pressure felt in the knees. Knees should NEVER extend past toes. Torso flexes forward slightly so that you can sit your hips back behind you. One good way to feel the weight shift correctly is to go into a squat, hold the position, and then tap your toes lightly. The weight automatically gets distributed to the butt and heels. If you perfect your form you may find that over time you can gtadually deepen your squats without any adverse effects
BALL SQUATS--perform squats with a physical therapy ball between your back and a wall. Feet should be in front of the hips. Bend knees (without extending past toes) and drop hips downward into a squat, rolling the ball along the wall as you go. Tailbone should point back to wall underneath ball as you squat. Drive up through the heels and butt to stand up. This is one of my favorite variations I do with my clients.
TUBING LEG LIFTS--step both feet on tubing about shoulder width apart. Hold the handles at your sides with arms relaxed. With knees soft, alternate lifting your legs from side to side. The movement is controlled and is not a big range of motion. This is one of the BEST butt and leg exercises ever and is great for the knees because it doesn't involve flexion. Keep knees soft through the entire exercise especially as you place the feet to the floor.
Hope these descriptions are clear. Let me know if you need more info.
As for the cardio, I think ellipticals are better intensity and will probably feel better on your knees because of less flexion required to do the motion. I am a little biased though. I love the elliptical and am not really into cycling. They both work your overall leg muscles. The elliptical will incorporate the butt a lot more and the bike will emphasize your quadriceps.
I have rheumatoid arthritis which is a lot different than osteoarthritis. Your kind is basically natural wear and tear of a joint so my tactics for dealing with my condition do not apply to your situation. The thing to do is to listen to your body. If your symptoms worsen two to forty eight hours after your workout you know you've done too much. I also would ask your specialist about chondrotin and glucosamine which help rebuild cartilage. Please check with the doctor though and avoid taking random supplements. I hope all this helps and I wish you the very best! Keep in touch.
Cyndie