When you use system or backticks or qx{}, the command is executed in a newly spawned shell, so setting an environment variable using one of these methods will not reflect to the calling process. Consider it to be equivalent to (I used $$ to show that it is the prompt of the sub-shell)

$ export A=1
$ echo $A
1
$ bash
$$ echo $A
1
$$ export A=2
$$ echo $A
2
$$ exit
$ echo $A
1
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So, those three are out.

The case of %ENV is way more interesting, as it involves scope and timing. Lets start with simple examples:

$ echo $A;perl -wE'say $ENV{A};$ENV{A}=2;say$ENV{A}';echo
$A
1
1
2
1
$ perl -wE'say $ENV{A};qx{echo \$A};$ENV{A}="B";say $ENV{A
};qx{echo \$A};'
1
B
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You can observe that the proces spawned with the first qx uses the original value stored in $A, and the second invocation uses the changed value, as you expect (if I read your question correctly), so no surprises there.

What will complicate matters is if those %ENV values are used in the startup phase of a module that you use. This implies that the value is used before you change its value. In that case, you should do something like

BEGIN {
    $ENV{test} = "B";
    }
use My::Module; # Which initializes with $ENV{test}
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Now the environment is set before it is seen by the module.

HTH