Hi,
What you can do is this:
Create a general sample product via the menu System>Products and set a price of $1 for it. You can put it in an unpublished category if you don't went to have it displayed by default on the products listings.
Then, create a custom field of the table "item" and of the type "text" via the menu Display>Custom fields (Business edition only) and restrict it to the unpublished category where your sample product is attached so that you don't get it on the product page of other products.
Finally, You can add a link like that in your products:
<a href="http://myshop.com/index.php?option=com_hikashop&ctrl=product&task=updatecart&quantity=1&checkout=1&product_id=XXX&data[item][YYY]=ZZZ">Order a sample</a>
where XXX is the id of the sample product, YYY is the column name of the custom field of the sample product and ZZZ is the value that you want in it for the current product (for example the name of the current product).
When the user will click on that link on a product page, it will add the sample product to the cart with the name of the product filled in the custom field and he will be redirected to the checkout in order to proceed.