Is STRATEGISE a proper word?

Except for your spelling it's a perfectly good word.
See this: http://www.answers.com/topic/strategize

VERB:
strat·e·gized , strat·e·giz·ing , strat·e·giz·es
VERB:
tr.
To plan a strategy for (a business or financial venture, for example).
VERB:
intr.
To determine strategies; plan: "a lot to think about and strategize about and anticipate" (New Yorker).

GB: American Heritage Dictionary claims that strategize has been around since the early 1970's.
There has been a lot of verbification going in the last 30 years or so in the business community. "-Ize" is a favorite ending. Management consultants who earn exhorbitant fees love to use the technique of word invention; creating new words for old ideas makes them sound so sophisticated and importa

You may use 'z' in your words but in Australia we use 's' in words like this, NOT THAT IT IS A WORD

That spelling is perfect English.
There is no letter zed in the word.
There is, however, the letter zee in the word translated into Ameriglish.
Hope this helps.
You're welcome.