By chart plotter you mean a ENC on a computer I assume?
The Lat/long might not be what they are looking for. Deep-sea with a pilot the pilot is using local knowledge of landmarks and so forth to navigate. To reduce the risk of a Cota / Cosco Busan type situation where the pilot steers the ship into a bridge the mate on watch is also required to maintain awareness of the ship’s position. That’s where on the river the requirement to mark on the chart when abeam (or passing under a bridge) come from.
In your case you are the pilot so presumably what they are looking for is a method to cross-check ( To cross-check is defined as to verify or confirm something using alternative sources of information). Because the ENC is using sat data from the GPS a lat/long from the same GPS is not a good cross-check.
Using radar or visual for a quick distance off is a better cross-check. Marking the chart requires that the correct chart be out on the chart table and that the navigator isn’t hypnotized by the display. It also leave a record that can be checked by auditors or the on-coming watch.
Similar discussion here Old school chart work