Another option is enzymatic cytochemistry, if fluorescense is not a must.
You can try Naphtol-AS-D-chloroacetate esterase. Quite specific for Neutrophils and is species independent. You can do the test in mouse, rat, human etc smears imprints as well as FFPE tissues.
Neutrophil bead uptake can also be used one of the biological markers for evaluating neutrophils, which eosinophils and monocytes would not be able to do.
for flow cytometric analysis of human blood you can use a combination of CD15 and CD16. CD15CD16 double positive cells are neutrophils, CD15positive CD16 negative are eosinophils.
For mouse blood use Ly6G. Combination with CD11b shows double positive neutrophils.