By removing the icon, you can separate viewing from modifying a record. You also reduce ambiguity from icon interpretation.
Since a common use of a list is to access a record and view its details, you could keep the actions as 'actions' which you have as specifically editing and deleting a record.
Try to remove ambiguity
If it's obvious that you can select and drilldown on the row, there's no need for a view icon, and in light of the fact that icons alone can be ambiguous, the less of them (without labels) the better.
(As a side note: The 'eye' icon is often meant for 'show/hide' in many contexts, which you definitely did not intend.)
Make selection easier
I don't know your use case, but if the most basic and non-destructive action is viewing details, make it easy to select a record, you can do this by signifying on hover that it can be selected, and you have an opportunity to increase the hit area.
See Fitt's Law re: selection
The aim of user interface design should be to reduce the distance from one point to the next and make the target object large enough to enable prompt detection and selection of interactive elements without sacrificing accuracy.
For validation, you can test with your users.