While saint Vyasa had categorized the Vedas for our ease of learning, then why do we have different dates in performing upakarma for each different Veda? Is utsarjanam on the same date for all or do the days differ?

We do not understand the question wholly, the opinion is not clear in your question on variation. Please state your doubt elaborately.
Vyasa has categorized the Vedas; the Smritis and Shrutis, based on the Veda, have ordained the various upakarma-s. One individual is not capable of learning all the Vedas. Hence, for the convenience of human beings, Vyasabhagavan has categorized the Vedas. For the respective Vedas which were revealed by a respective sage, we perform the upakarma on the period specified for them.