Polite Way of Saying "I can't...(answer the phone)" (しかねる vs. できない)

Question

I'd like to ask about a polite way to say "I can't (do something for you)". I'm sure the answer will depend on the context, so specifically, I'm curious about how to convey "I won't be able to answer the phone from..." over email in a business setting.

My attempt is:

海外旅行のため、1月10日から21日まで電話で対応しかねますので、大変ご迷惑をおかけしますが、メールでご連絡をお願い申し上げます。

My specific questions are:

1. Is しかねる valid for politely giving this type of "excuse" for why you can't do something?
2. Can できない also be used for politely giving this type of "excuse" for why you can't do something? (e.g., "電話で対応できませんが…")
3. If neither of these are polite/appropriate in this case, what is a better alternative?

Answer 1

1. Is しかねる valid for politely giving this type of "excuse" for why you can't do something?

出来かねる or 致しかねる is better. and I think, it's better not to mention about the detailed reason.

2. Can できない also be used for politely giving this type of "excuse" for why you can't do something? (e.g., "電話で対応できませんが…")

Yes.

3. If neither of these are polite/appropriate in this case, what is a better alternative?

"1月10日から21日まで休暇を頂くため、お電話での対応を致しかねます。恐れいります恐れ入りますが、ご入用の際には、メールにてご連絡下さいますよう、お願い申し上げます。"

Answer 2

The simple, polite way to say it is:

１月１０日から２１日まで海外旅行しますので、電話は使えません。メールでご連絡ください。

That's the way most people will write it in an email. However, if you're being very humble, you could say something more like:

１月１０日から２１日まで海外旅行しますので、電話はできません。メールでご連絡いただけないでしょうか。

Which is, more or less, "I'm going to be away on a trip from the 10th to the 21st, and won't be able to use my phone. Is there any way I could have you contact me via email?"