Hi,
yes this is possible but require a template override, you can create a radio field (for example with alias "email_button" with 2 options like:

1|No

2|Yes

Based on the value of this field you can create a template override of profile page that show button if the value is 2:
- Copy file from /components/com_jsn/views/profile/tmpl/default.php to /templates/your-theme-folder/html/com_jsn/profile/default.php (create folder first)
- Open the new field
- At line 47 replace this with code

<?php if ($this->config->get('profile_contact_btn',1) && JFactory::getUser()->id != $this->data->id) :

with this

<?php if ( (int)$this->user->email_button == 2 && $this->config->get('profile_contact_btn',1) && JFactory::getUser()->id != $this->data->id) :

Basically I have added a new condition to show the button

(int)$this->user->email_button == 2

NOTE: This code is not tested and not supported, this is only for example purpose.