Use another servers mail()

i was wondering i can use another servers mail() to work with with wordpress.

the server im using to host wordpress doesnt allow mail, stmp doesnt work either…however there is another website that does gives me free hosting with the mail function.
before i used wordpress i set up a contact form and uploaded the file which called the mail() on the other server and it worked like a charm
as in i changed

<form name=”contactform” method=”post” action=”send_form_email.php”>
<table width=”450px”>
</tr>
<tr>
<td valign=”top”>
<label for=”first_name”>…

to

<form name=”contactform” method=”post” action=”www.my-other-site.com/send_form_email.php”>
<table width=”450px”>
</tr>
<tr>
<td valign=”top”>
<label for=”first_name”>…

and it worked like a charm

common sense dictates that i host wordpress on that server but ive been there and it comes with its fair share limitations and issues