I will also second DBD::SQLite. You can ease the transition using Tie::Hash::DBD, which should be a drop-in replacement for SDBM.

use Fcntl;
use SDBM_File;

tie my %hash, "SDBM_File", "file.sdbm", O_RDWR | O_CREAT, 0666;

-->

use Tie::Hash::DBD;

tie my %hash, "Tie::Hash::DBD", "dbi:SQLite:dbname=file.sqlite";
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Read the manual for persistence options.