I mean, the situation you've explained doesn't sound forced. Sounds like you have two really awesome sets of Far Side tomes and you'd like to share one with somebody, why not a person that's apparently into comics and has a taste for Gary's style and humor that shine through in your own series... oh wait the perfect match sounds like one of your followers. ;D
Especially if you explain your contest akin to that with a side note of I'd also like to promote my own series, it comes across genuine and not gimmicky.
All the better! These kids gotta know the awesome-ness of Far Side. XD
Or you could do something like runner ups in the drawing get sketch cards or digital art requests. Something quick and easy and personal.
Contests can be a mixed bag. They take time and work to promote and get the word out that you're running a contest. Offering an extra entry ticket into the raffle for sharing the contest through social media can help spread that word a bit more. Also consider looking into sites that can help manage the contest for you. Gleam.io is a good one that I've used twice. It's possible to do all you need with the free options, even setting up a custom raffle entry for those that have subbed to you on Tapastic. (just ask participants to give their tapastic user name in the custom field).
The few experience I've had with contests have been positive. Remember to keep it simple and easy for you to deliver on. International shipping can cost a LOT! Maybe offer a digital version of the prize for international winners if possible.