There is also the Knee Injury and Osteoarthritis Outcome Score-Quality of Life (KOOS-QoL) subscale:
Vennu, V., & Bindawas, S. M. (2014). Relationship between falls, knee osteoarthritis, and health-related quality of life: data from the Osteoarthritis Initiative study. Clinical interventions in aging, 9, 793.
Some researchers have used the TUG Test (Timed Up and Go) although it isn't specifically for OA:
https://www.cdc.gov/steadi/pdf/tug_test-a.pdf
e.g. :
Beauchet, O., Fantino, B., Allali, G., Muir, S. W., Montero-Odasso, M., & Annweiler, C. (2011). Timed Up and Go test and risk of falls in older adults: a systematic review. The journal of nutrition, health & aging, 15(10), 933-938.
There is also the Spring Scale Test, but again not specifically for OA:
DePasquale, L., & Toscano, L. (2009). The Spring Scale Test: a reliable and valid tool for explaining fall history. Journal of Geriatric Physical Therapy, 32(4), 159-167.
The Spring Scale Test employs repeated incremental 'predictable" perturbations to quantify rear and forward stepping threshold and stepping limits milestones employing % total body weight measure.
10 % TBW force value and single step response at 10 % TBW force value are strong discriminating measures for ID fall risk in active , community living, older adults
I think it is good to use functional reaching test since the patient with knee OA will be able to stand for short time before the aggravation of the pain.