I store my tomato seeds in the fridge but I don't know if I should store any of my other seeds there year round. I have watermelon, squash, okra, cantaloupe, and cucumber seeds that I am inquiring about. If I stored these seeds in the fridge or freezer, would it improve the seed's life before germination? I currently do not keep these seeds in air-tight containers and I do not use silica packs. I however, keep them in the containers that contain diabetic test strips away from heat/cold and sunlight.
I store my bean, corn, and peas in air-tight glass jars with silica packs underneath the cabinet away from heat/cold and sunlight. These will last several years by doing this method.
I have been storing all the seeds you mentioned in the freezer for years. A lot of them I freeze in the original package in a zip lock bag. Since my diabetic supplies started coming in those nifty snap top bottles, I put my small seeds in them. Handy to carry to the garden. The seeds I save like green beans, okra, and butter beans, I put in jars like you. Every thing goes in the freezer. I planted a new type of okra this year a friend gave me and they had been in the freezer for five years. I got a perfect stand the first time. He planted seed from the year before and like to never have got a stand. My theory is that if the seed germination is good going into the freezer it will be good coming out. Just a red neck comment he has learned from long experience.