Based on your description, it is unlikely these plants are worth saving.  The growing season is still early and you have plenty of time to reseed and start over.   Dish soap solution may have  caused foliage burn that you see.  When you get the new cucumbers to about 4-6" in height, consider prophylaxis against aphids with neem oil.  Inspect plants 2-3 x /week and if there is a light infestation with aphids spray them off with a gentle water spray.  If that fails, then use insecticidal soap, but purchase it at a nursery or hardware store rather than make it at home.  Below are two references from the University of Maryland Extension web site.  The first covers growing cucumbers and the second discusses aphid infestation and its management. 

https://extension.umd.edu/resource/cucumbers

https://extension.umd.edu/resource/aphids-vegetables

Although most aphid varieties live on foliage and feed on the leaves, the grey-white root aphids live in the soil and also lay their eggs in the soil. Although they slightly vary in appearance from the stem/leaf aphids, the damage they cause is similar resulting in leaf and plant wilt and die back if untreated.  Although it sounds like you are dealing with stem/leaf aphids, I would recommend changing the soil in the container just to be on the safe side.  Even if you detect aphids early after germination, the measures that I previously outlined should control them.  Good luck and let me know if you have persistent problems.