Doing a game doesn't guarantee that fun will be had; in fact, I'd go so far as to say that dutifully cranking or cracking one out might create the impression that you are just trying to fill time (which you do say is one of your explicit concerns). Are you team-teaching with burnt-out Japanese teachers of English or something?
If so, just because they want a break from doing anything doesn't necessarily mean that you should pull your hair out with worrying how to meet their exact demands/specifications, or feel that you need to be "serious" with the "fun-making" or forget about teaching incidentally.
That is, games to me occupy a strange no-man's land between being genuinely fun, silly, open, naive, innocent etc and being VERY "serious" (perhaps I should say passionate instead, it has better connotations) about language, (real) communication etc.
I have always been amazed at how communicative approaches think games are "easy" options, easy to play, therefore fun rather than frustrating: they forget that a game has social purposes other than to win, and that functionally participating in and fulfilling/enjoying the game for those other social purposes often requires far more "incidental" language than the exponents for "playing" the game have anticipated. Of course, some games may require or demand silence and concentration dues to their rules or nature (bluffing in poker, appreciation of what is really being "said" in bridge etc), but for most games, just playing them slavishly by the rulebook is not the whole story.
So, I would be trying to think of something that allows attention to move between you (because you want to introduce yourself and allow them to get to know you, make an impression on them, get them liking you hopefully), them (because you want to get to know them, or they might think of a zillion things to say), and "the game"; to me, the game is all around us, in what we choose to say in often playful response to what we've been asked or told. I think of Japanese TV shows where people often really do seem to be having a lot of fun with the language, testing or even flouting conversational maxims etc in the course of sticking to the generally probably rehearsed general script or completing their tasks. (I don't understand much Japanese, but I do enjoy watching those shows sometimes!).
I think if you can enter the class and stand there looking like you want to have fun, any game is incidental (but it could help provide a basis for discussion). I'd maybe try to find some interesting stories or pictures from your life, the news, strange/crazy/zany facts etc, and make a few notes about how they could be structured to allow you to say something-get the ball rolling-keep it moving-prompt the students to say something-anticipate their needs etc. This would be a whole-class activity, perhaps with a sheet with key pictures/phrases (speech bubbles coming from mouths in photos?) etc, nothing too linear or "obvious" in terms of only 1 then 2 before stage 3. If the discussion and give-and-take really took off I'd be tempted to leave my sheet on the desk and move away from it, towards the topic (and people) who were engaging everyone. If your JTE is any good they will help rather than hinder you in all this.
Actual paired activities leading on from this kind of intro stuff include questionnaires, matching "exercises", complete the sentences with a word or thought etc. I'd probably save the actual games for later...and designing ones that encourage or necessitate the use of much natural (connected) language is actually quite difficult! There are so many other ways to say things, so many other things to say, and so many coping or avoidance strategies, in addition to which, students may have purposes or agendas other than to play your "silly games" when they often have agendas of their own to discuss and pursue (as I've implied).
Basically, I think wordplay, or rather, "meaning play"*, is a good way to go about setting up a nice classroom atmosphere. Show people that you want to joke with them, and that they are welcome to joke with you too (it'll help everyone relax if nothing else, worrying about the language and pedagogy is the second, not the first step once you're actually inside the classroom).
Good luck anyway!!!
*If you started punning or telling native-speaker jokes you'd lose them. I'm talking about deliberately misconstruing their meanings when whatever they've said "tickles your fancy". Of course, if you aren't the type who can be spontaneous this approach won't work so well, it certainly can't be forced through calculation, that would always be a bit too slow, it's ultimately gotta stem from an instinct, an instinctive reflex, your natural "behaviour" ("bad", "naughty", "joking", "cute", "coy" etc behaviour - be ready to assume many different "roles" to "teach" in a meaningful way! Language may ultimately just be a code or data, but cracking its use and then using it ourselves requires more than just logic and rules, there are social relationships being acted out and evolving through it too e.g. the desire to make and win over friends. Not saying that being a joker all the time will necessarily
maintain or keep friendships going, a need for affection and reassurance can get wearing, especially when a person really does need to get serious).