There are a lot of factors: area, water temp, how often the boat will be moved. You said a one month cruise; assuming you will be moving daily, that is actually better for keeping growth off. Warm temperatures seem to create more problems than colder water. Different waters seem to have different problems - slime, the furry plant stuff, and barnacles.
When we first picked up our boat, we cruised for 6 weeks in the Pacific Northwest (colder water, moving nearly everyday) and a simple rinse was all the bottom needed when we pulled out. About 10 days in the warm Gulf water and critters were already starting to attach. I pulled the boat into shallow water and scrubbed the bottom - it was good for another 10 days or so. After a few episodes of that, I pulled the boat out for a bottom job. I guess I don't understand the reluctance to bottom paint; all our boats have had it. We use an ablative paint that remains effective even when pulled out to trailer. It needed touching up after about two years of very regular use.
Yes, I've gotten paint on my hand when messing with the boat on the trailer. I use this new-fangled stuff called "soap" and it cleans right up.

I've had hard bottom paint sprayed on our trimaran (to keep the bottom smooth for performance), and it worked fine, too. Check with boat yards in the area you intend to cruise and see what they recommend.
If you plunk a boat in warm water for a month and don't move it, I'd expect some crud on the bottom. Run your hand on the bottom after a week or so... you can feel the slime, and you can
really feel the barnacles. I've never noticed a performance hit from bottom paint, but the crud on the bottom will really cut into your efficiency.
A month of cruising sounds like fun... a little bottom scrubbing is a very small price to pay for those good times.
Have fun!
Best wishes,
Jim B.