There are many flaws in your proposals, Asker, that immediately betray a non-native writer. I'll try and help you below with as many of them as a can.

First of all, it would never be 'the steel clamp' — that could only be the case if there were some specific one, but we already know there isn't one! Also, mentioning twice the clamp that is not being used and only once the clamp that is being used seems a bit pointless; and finally, the whole thing is very clunky and awkward. We also need to know what this text is for, its overall context — this will in particular determine the suitability or not of your expression "we did not use..."

In order to prevent the CFCC from crushing when the steel clamp is comprssed, we did not use a steel clamp but an aluminum clamp to grip the outer layer of the electric wire.
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To avoid the CFCC's being crushed if a steel clamp were used, we have chosen to use an aluminium clamp to grip the outer sheath / jacket of the (electrical) cable

Choice of wire / cable depends on the context, and it is unlikely to be necessary to specify 'electrical', since cables are rarely used for anything else (unless it is important to make the distinction here).

The text does not explicitly state WHY an aluminium clamp would crush less than a steel one? Logically, I'd assume because it is either bendier, or else simply cannot be tightened as much; although this is clearly a deficiency in your source text, knowing the reason would help make your translation better.

Note the correct use of articles, and the elimination of 'did', which should only be used here in certain specific circumstances — e.g. if this were recounting some kind of laboratory procedure.