You want approach b, or at least a modification of it.
You don't have to divide all of your predictors by 10--just the ones that make sense to do so. It is totally legitimate to multiply some predictors by 100 and others by 10, for example. It won't change your results, p-values, etc. at all--just how the odds ratios are interpreted.
Taking approach a will just throw away information in your predictor. There is no way to interpret any type of regression parameter from an ordinal predictor. They need to be either numerical or nominal.
Taking the log of X (a predictor), is used either to change the relationship between X and Y from a linear one or to pull in outliers in X.