Create a transaction A
Output - To whoever
Change - To you.
Fee - To Random Miner.

Send change in transaction B
Output to Mining pool you want to support.
Change - None.
Fee - To Random Miner.


This way the mining pool is incentivized to make sure both your transactions end up in blocks, but it doesn't really matter who puts them in.
You'll just need to set your fees low enough to get your transaction relayed, and if you can submit your transaction directly to a miner you might even be able to avoid needing to do that.