Learn French: Nous ferons l'installation nous-mêmes au cas où le technicien annulerait. - We will do the installation ourselves in case the technician cancels.

When attached to a personal pronoun to mean "oneself" (like "ourselves" here), you must connect it with a hyphen. Because nous is plural, même acts as an adjective here and must agree in number, so it takes an 's'.

Could nous-mêmes mean "even us" in this context?

No, because it is attached with a hyphen after the pronoun. To use the adverbial "even" (meaning "Even we will do the installation"), you would place même without a hyphen before the subject: Même nous ferons l'installation...

Uncertainty usually triggers the subjunctive. Why is annulerait in the conditional?

This is a famous exception that catches out a lot of learners! The phrase au cas où (in case) is always followed by the conditional, never the subjunctive. This is because it introduces a pure hypothesis rather than a subjective feeling of doubt or necessity.

Is it more natural to say ferons l'installation rather than just using the verb installerons?

Both are completely natural and correct. French frequently uses the verb faire followed by a noun for practical tasks, chores, or professional services (similar to faire le ménage or faire les réparations). You could definitely say Nous l'installerons nous-mêmes instead.