The word that determines the form of perform is choice not but. You have the choice to do something, not doing it. So it has to be:
You have no choice to perform the test yourself.
You cannot say:
You have no choice performing the test yourself.
You can use a gerund, however, if choice is followed by in:
You have no choice in performing the test.
This aspect of language has been termed "grammatical collocation". Here is part of the entry on this term in the Oxford Dictionary of English Grammar (p70):
Grammatical collocation: a construction where a verb, adjective, etc.
must be followed by a particular preposition, or a noun must be
followed by a particular form of the verb (e.g. account for; afraid
of; the foresight to do it (not *of doing it).