Difference between "другого ..., кроме как ..." and "другого ..., как ..."

Question

I just said in conversation:

Похоже, у меня не остается другого выбора, кроме как помочь им.

I'm not sure if I could just as well have said "другого выбора, как помочь", dropping "кроме".

Answer 1

Although they are both possible, I disagree that they have the same meaning.

Expression with кроме discusses how you can't not help them -- выбор refers to the choice between helping and not helping, i.e. not helping is initially an option, but it's eventually rejected in favor of helping.

Expression without кроме discusses how there's no other way of helping them -- выбор refers to the choice between all the hypothetical ways to help them, i.e. not helping is not an option in the first place.

To sum up,

Похоже, у меня не остается другого выбора, кроме как помочь им.

means

Apparently, I have no choice but to help them.

On the other hand,

Похоже, у меня не остается другого выбора, как помочь им.

means

Apparently, I have no other option how to help them.

As mentioned by Баян in the comments, the last Russian sentence is a poor choice of words, and more natural way of saying would look like ...не остаётся другого способа помочь им. Still, if you encountered у меня не остаётся другого выбора, как помочь им, and you totally can, you should definitely take it to mean "...I have no other option how to help them".

Answer 2

Both variants are grammatical and have the same meaning. The first variant is more explicit, and you can stick to it for that reason: there could be other similar phrases where как would rather mean how:

я не знаю другого способа как тебе помочь.

(I do not know another way how to help you)