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If you want it to return to the variegated foliage, then yes, prune back all the green-leaved branches as far back as possible and leave only the variegated ones to encourage them to grow. The green foliage will take over if not pruned back regularly. Here is more advice on pruning Euonyous:

https://www.gardeningknowhow.com/ornamental/shrubs/burning-bush/pruning-burning-bush.htm

It is much easier to start from cuttings, and to do this when it starts to warm up in spring. Take from the new growth for easier rooting. I will include an articlefor more on this subject here: https://www.gardeningknowhow.com/ornamental/trees/tgen/how-to-root-cuttings-from-various-shrubs-bushes-and-trees.htm

If you choose to do it from seed, it is necessary to know the steps to break its stubborn dormancy. This website explains how to do so: http://www.treeseedonline.com/store/p136/Spindle_Tree%2FCommon_Spindle_%28euonymus_europeaus%29.html

You have nothing to worry about except finding a new yard man. Euonymus fortunei is considered an invasive groundcover. If you ever try to get rid of it, you'll discover the extensive root system. Put down a 2 inch layer of mulch to hold the soil in place over the winter. There is no need to remove it in spring. It will compost in place and will not hinder the regrowth of the wintercreeper.

Is this one one plant or all of them? Can you include pictures, and more information about the area, and any changes that have happened recently?

Most euonymous will tolerate very heavy pruning. This can help to regenerate old shrubs. Some species are even considered highly invasive in certain areas.

I would recommend wiping the cut area with peroxide, instead of soap. This will leave no residue behind, as it will dissolve into, both, oxygen and water.

I believe an eternity is pretty darn close. The Dept of Agriculture (US) lists its lifespan as 250 years.