Can leg claudication cause random sharp pain?

Unlikely: Leg claudication is a cramping muscle pain, and/or numbness/pain in the foot which comes on with exercise and improves with rest. Claudication symptoms are very predictable and reproducible. The random sharp pain you describe is unlikely to be claudication pain.

No: Claudication that is related to a lack of circulation to any muscle group is experienced only when that muscle group is being exercised. Therefore it is reproducible and constant in its presentation. The pain does not radiate and does not come out of the blue. Clarification pain also subsides when the exercise stops and rest begins.