If you want the errors to be kept till after the loop, maybe try a $SIG{"__WARN__"} handler

d:\temp>perl -e"$SIG{"__WARN__"} = sub {push @err,$_[0]; print STDERR 
+$_[0]}; while(<>) {1};print qq<---\n @err>" file1 file2 file3
Can't open file1: No such file or directory at -e line 1.
Can't open file2: No such file or directory at -e line 1.
Can't open file3: No such file or directory at -e line 1.
---
 Can't open file1: No such file or directory at -e line 1.
 Can't open file2: No such file or directory at -e line 1.
 Can't open file3: No such file or directory at -e line 1.

d:\temp>
[download]

This is perl 5, version 32, subversion 1 (v5.32.1) built for MSWin32-x64-multi-thread

you can also only record the filename by pushing $ARGV instead and control what the user sees.

furthermore you can scope the handler with local tightly around the relevant code

{ local $SIG{"__WARN__"}= sub {...}; while(<>){...} }