No one jumped on your question, did they? Maybe no one knows. I don't. I assume you mean holding dumbbells. I think anything like that would help, though. But probably no good without the dumbbells. If it hurts, quit it. Another thing that's good is one-legged deep knee bends. You can either do them on a chair with a finger on the wall, or free standing with one leg held out in front of you. I once did 200 of those latter ones, in one set, long long ago. Try sets of 20, alternating legs.
Also, do hyperextensions with your hips on the arm of a sofa. Pushups are great. If they're too easy, shout Airborne! as you clap your hands. Do situps lying on the floor with thighs at 90° to your trunk, your calves on a sofa or chair and someone sitting on your shins. That's great for hip flexors. You can also do one-legged calf raises with your toe on the edge of a chair or block of wood. Hook your other toe behind your Achilles tendon and put a finger on the wall.
the only real help they'll give is strengthening your knees and hip flexors. Maybe some ankle strength as well. If you've got the time nd energy you can weight train your whole body without a gym. Why can't you weight train?
You can do walking lunges without holding dumbbells and chances are you'll feel it in your glutes the next day or two.
To the OP: The jury is still out on whether strength training improves cycling performance. I'll save that debate for another day. To specifically answer your question, in this case I would say it's worth a try. You could do a few sets of lunges and it would take you 15 minutes max. Is 15 minutes going to significantly take away from your riding time? I doubt it. I also doubt that recovery time for the lunges will be high enough to take away from your riding schedule. In other words, you don't have much to lose by trying.