The best way is to already have the information. Do you have no audit trail of any type at all which shows additions/deletions relating to the file? How does anyone know nothing goes missing/gets erroneously added?
For know how fast a VSAM files is growing, the record-count is a pretty arbitrary measure anyway: you'd need to relate "records" to "space supporting records" if KSDS - CI and CA freespace being the most important. If all inserts are in one part of the file there may be significantly different new DASD usage than if they are scattered "randomly" across the file (and it could be either less or more used, depending...).
To read an entire VSAM dataset of any size just to get a count of records because someone feels it is important... look in the manuals and find out how VERIFY works...
Are you lucky-enough that a "client" is going to be paying for this and they'll probably not question it?