Answer: You would absolutely not see any influence on this year's produce taste or shape on your melons/cucumbers by planting the different plants close to each other.
Any effect of close planting and crossing would be seen the following year if you saved seed and then planted the seed you had saved. And, only plants of the same species can cross so even then your problems would be very limited. (For example, pumpkins and squash can potentially cross. But watermelon does not cross with muskmelon, cucumber, squash, or pumpkin. Cantelope and cucumber will not cross.)
Any odd plants are the result of the seed used to start them or a label problem at some point in the growing process or possibly the growing conditions this year. If you purchased the plants, perhaps their seed strains were not pure or perhaps the seedling plants were accidently mixed up before sale. Or, sometimes the soil and water and weather conditions can combine to affect flavor (not that they would all taste the same, but they can all seem bitter, for example...)
Here is a little more information about the crossing you may find interesting. You may need to cut and paste the complete url into your browser to make it work correctly.
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