First, wegen requires the genitive, so it must be

Hallo, wegen des Bluttests, ...

For the question which word to use, yes, you can use either für X or wegen Y, both would be correct. Which one would sound more natural would depend a bit un the exact wording.

(more to come)

First, wegen requires the genitive, so it must be

Hallo, wegen des Bluttests, ...

For the question which word to use, yes, you can use either für X or wegen Y, both would be correct. Which one would sound more natural would depend a bit un the exact wording.

The version with wegen would be the best choice as an introduction to another complete sentence. Examples:

Wegen des Bluttests: Darf ich da vorher etwas essen, oder muss ich nüchtern sein?
(For the blood test: may I eat something before or do I need to have an empty stomach?)

Wegen des Bluttests sollte ich mich bei Doktor Müller melden.
(With respect to the blood test I should report to Doktor Müller)

Wegen des Bluttests hätte ich da noch ein paar Fragen
(With regard to the blood test, I still have some questions)

In your concrete example with direction, wegen is also possible, but I would probably rather say

Für den Bluttest, muss ich da nach rechts oder links?
or even
Zum Bluttest, muss ich da nach rechts oder links?

But that is a matter of style rather than a matter of right or wrong.