This (ISTA and AOSA) should be sufficient standard tests. But may also do direct germination on soil or cloth (non-standard but practical) . Others start with pre-soaking to check proportion of floaters (empty or less dense or of lower vigor).
For Cotton Germination follow ISTA germination test procedure like BP (between paper method) and sand tray emergence method.
Further for cotton seed vigor assessment ,you can try the method like "cotton cool test".For this expose the seeds to 18 C and later seeds will be incubated in 25 C for ISTA recommended days.Later seed counts will be done.
we use standard between paper method (ISTA) for viability assessment of cottonseed in our lab. but at constant 25C, however, if viability is low, then we perform other procedures including invigoration.