I want to have my own site to convert currencies euro dollar and so on. I prefer Wordpress because of the mobile friendly themes, seo plugins and all the other stuff. Is it possible and recommended to use Wordpress to code and implement just the converter into the website or is that very risky and could mess-up the entire theme ?
Why don't you use some javascript code from some site which provides it? Probably in exchange for a link...
Google won't rank you for this term. It got its own resources doing this, much more trusted. This would only be a functionality for your website users. Copy paste javascript would be enough...