The short answer is make each script exit with 1 for success or 0 on error and then

do '1-search_user.pl' or die;
do '2-prepare_2update_user.pl' or die;
do '3-backup.pl' or die;
do '4-run_update.pl' or die;
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But that isn't really the best solution. I would either combine the four scripts into one script or put the functionality into a module. The first solution looks like

search_user();
prepare_2update_user();
backup();
run_update();

sub search_user {
    ...
}
etc
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Are these scripts used elsewhere? If so then I'd go for a module and the script would then look like.

use MyModule;

MyModule::search_user();
MyModule::prepare_2update_user();
MyModule::backup();
MyModule::run_update();
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In either case each function throws it's own exception so you don't check for errors if all you want to do is exit.

To get started with modules see Simple Module Tutorial

The script executes sequentially and it can be run from cron, you will need to ensure that it can find the other scripts, environment variables may not be set so do '/path/to/script' or push @INC, '/path/to' may be necessary.