Perhaps the add-on expr module allows this? A cursory glance through the docs didn't show any such capability.

You generally will build the entire data structure ahead of time, but you don't have to. Another documented option - the associate parameter to the new() method, allows you to associate any object that provides a param() method to the given template. Then, what HTML::Template will do when it needs a parameter (for a TMPL_VAR, TMPL_LOOP, or TMPL_IF/UNLESS), is check the following places in order:
1. Its parameter stash
2. The associated object(s), in the order they were associated in
3. If within a loop and GLOBAL_VARS has been specified, it will check the next outermost scope, repeating the same actions
The param() method is expected to return undef if it doesn't handle that parameter name. (Make sure you specify the case_sensitive option or be case-insensitive yourself.)

So, you can now do something like:

package My::Associated::DBH::Wrapper;

# Called as:
# my $thingy = My::Associated::DBH::Wrapper->new(
#    sth => $sth,
#    param_name => 'Foo',
# );

sub new {
    my $class = shift;
    my %args = @_;
    bless \%args, $class;
}

sub param {
    my $self = shift;
    my ($param) = @_;

    return unless $param eq $self->{param_name};

    my @values = $self->{sth}->fetchrow_array;
    return unless @values;

    return $values[0];
}
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Then, when you build your template, you can go ahead and do this:

my $template = HTML::Template->new(
    filename => 'my_template.tmpl',
    associate => [ $thingy, $query ],
);
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