Squash and cukes are OK without refrigeration, but some suggestions would be an extra refrigerator, coolers, cover with damp towel...
I moved from using coolers with ice to extra refrigerators (used on the warm side to conserve energy), to using an air conditioning unit with a coolbot and it works great.
www.storeitcold.com

Here is a link that might be useful: Coolbot link

Get a used commercial fridge-at least a two door or seriously think about building a very well insulated room and go the cool bot route. Actually doing both is optimal as some things need to be kept much colder than other things.

Having good refrigeration will make your life a lot easier and probably be cheaper than buying ice to keep things cool in coolers (and if you are doing this seriously you will find you will need a lot of coolers to keep things cold).

I remember when we got our first commercial fridge (a 1951 Eskimo)-it was a beat up fridge we got for about $25 from a local food co-op that was upgrading. getting refrigeration made life far easier and the produce quality went up greatly. It sure was nice not to have to spend 18 hours before Saturday AM market harvesting and cleaning produce. It was also nice to no longer have to deal with molding berries in summer because the basement was nowhere near cold enough to store them for more than 18 hours. or cleaning out coolers several times a week and all the other gyrations we made to keep the produce in decent condition before we had refrigeration.

Until this year, I never refrigerated my produce. I just did not have the room. I have used 2-lt soda/pop bottles frozen in cooler. This had it's down sides. Green beans got 'fuzzies'. We would pick tomatoes early in the week, always picking just barely under=ripe, giving us more time to pick everything else. The day before market (we have 3 market days) we would pick squash/zucchini early in the day, before the dew left. The last thing picked was beans, due to not wanting to have the 'rust' on the beans.

We use a large cargo van to transport to market. The late afternoon/evening was 'packing the van' time. All produce was placed on tables in the shade of several trees after picking. One thing I have figured out is to cover the veggies in the van after loading so that the condensation doesn't rise to the ceiling and drop back down as rain getting the beans wet.

One of my sons was given a refrigerated room from a food bank. Bad thing, it was taken apart when he got it. Now we have to figure out how to put it back together and hopefully it's all there.

I have not done it yet, but I was thinking of making a room that is well insulated and installing one or two window air conditioners. Then I could set them for whatever desired temperature.

well i have a 10x20 storage building, no windows, r30 insulation on 3 walls and the ceiling(the 4th wall has r12 and is shaded all day)i have a window air conditioner i put in the north wall and so far it seems to keep me at 55 degrees. i figure beans can go in a cooler and most other things should keep overnight not sure how the okra will do at 55 but im gonna try it and see, if i pick it around 7pm and go to market the next morning at 7am??? im gonna try it with a few pounds and see what happens, squash, tomato's and cucs should do fine at 55 degrees and if i can just get an old refrigerator to keep beans and shelled peas in i think that may work depending on how many beans i have, that cool bot thing not too sure bout that it says nowhere what it actually does, yea it says how much of a miracle tool it is but nowhere does it say what its actual function is, looks like an over priced temperature sensor, any insight on what it does

55F is not cold enough for a whole lot of things such as green beans. it is about perfect for tomatoes, okra, eegplant, basil and other things that hate cold. But beans, greens, roots, fruit, etc., need it at least 42F and 34F is optimal.

Here is a link that might be useful: Cool-Bot