The easiest way is the string form of eval:

if ($^O eq 'WhizBang Unix') {
    eval "use Module::WhizBang;";
    die $@ if $@;
} else ...
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As the documentation tells you, use is basically equivalent to

BEGIN {
    require Module::Name;
    Module::Name->import();
};
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so you can avoid the string eval (which is safe in this instance) by using

BEGIN {
    my $module = "Module::Name";
    my $module_file = $module;

    # Translate module name into file name
    $module_file =~ s!::!/!g;
    $module_file .= '.pm';

    require $module_file;
    $module->import();
};
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