You can use index to find the position of the "1" and the four-argument form of substr to replace it.

knoppix@Microknoppix:~$ perl -E '
> $str = q{mystring123456};
> substr $str, index( $str, q{1} ), 1, q{};
> say $str;'
mystring23456
knoppix@Microknoppix:~$
[download]

I hope this is helpful.