It's true that cucumbers are best planted as seed in the location in which they will grow. There are however many considerations to work through when contemplating a relocation.
What I'm thinking in this situation...
Leave in small pots:
- no risk of transplant shock;
- water daily;
- apply tonic (such as seaweed emulsion) weekly;
- apply fertiliser fortnightly;
- greater risk of plant disease;
- expect smaller plants with low yield / small crop.
Transplant to large pots or into ground:
- risk of transplant shock;
- water weekly;
- apply tonic (such as seaweed emulsion) fortnightly;
- apply fertiliser monthly;
- lower risk of plant disease;
- expect larger plants with higher yield / larger crop.
Also what season are you currently in? Heading into winter or summer? I'm assuming the latter. So you should be in peak growing season, ensuring the plants are at their greatest potential for adaptation.
Ideally the plants would go into the ground or those 5 gallon buckets you use for your tomatoes, or larger if possible. The more good soil you can provide for your plants the happier and more resilient to pests it will be.
Untangling the vines would be a difficult task, however necessary if you want to transplant. You'd be better cutting the tendrils that have latched onto the trellis and cutting the vines that have wrapped around the trellis. This may seem difficult to do but the plant will heal and will, for the transplant, provide a smaller plant that will have a greater chance of recovery.
What you'll be attempting to achieve during transplant is minimal root disturbance. Do not water for at least a day before transplant. A dry soil is more likely to hold together than a wet soil when removed from a pot.
Make sure that if you decide to transplant, have everything ready so all that is needed is to turn your cucumbers out of their existing pot, carefully place in their new larger pots, carefully fill soil around the edges and finally water in.
A reminder that what you'll be attempting to achieve during transplant is minimal root disturbance.
When you water in the transplanted plants, make sure you include a liquid tonic such as seaweed extract or bacterial "probiotic". This should help your plant minimise "transplant shock" and repel any pests and disease.
Lastly it's worth mentioning an alternative - that you could also set up the new larger pot/s, buy two new advanced cucumber plants from a local nursery and plant your existing and the new plants at the same time, so that if you did lose the older more advanced plants at least you would be likely to retain the smaller less advanced plants.