Or you could do it the old-fashoned way:

BEGIN {
    *CORE::GLOBAL::sysread = sub (*\$$;$) {
        # whatever
    };
}
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If you want to limit the damage, you can localize the effect to a dynamic scope:

{
    local *CORE::GLOBAL::sysread = \&mysysread;
    # do things that call builtin sysread
}
# no more replacement from here on
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