aa=

It's possible that USCIS may deny the petition, but I could not find any official USCIS policy stating that a self-affidavit would not be enough to address the issue.  On the other hand, there is clear DOS policy about K1 visa ineligibility for this situation -- https://fam.state.gov/fam/09FAM/09FAM030205.html#M302_5_4_B_3

9 FAM 302.5-4(B)(3)  (U) Applicants Whose Marriage Violates State Law
[...]
Additionally, if an applicant intends to marry another individual in the United States in a state where such marriage would be legal but will then reside in another state where such marriage may violate that state’s laws, the applicant may be ineligible under INA 212(a)(3)(A)(ii).
 

you could marry in another state but your AOS interview will be in Texas if your cousin still lives there
plus ,  after marriage cousin will not be able to add u to any state run plans (even our insurance laws are state to state)
 
So, be ready to hire a good lawyer , pay thru the nose ,  and go thru a lengthy legal battle if your cousin continues to live (with u ) in Texas as the following shows
 
Matter of Balodis, 17 I&N Dec. 428 (Reg. Comm. 1980)
 
 At issue was a K fiancée petition filed by a U.S. citizen petitioner on behalf of his first cousin. The petition was initially denied because the state of the petitioner's domicile, Michigan, prohibited marriages between first cousins. However, the INS regional commissioner reversed that decision because Michigan recognized marriages between first cousins when they were lawfully entered into outside of the state. Because the regional commissioner concluded that the petitioner and beneficiary could legally marry outside of Michigan, he reversed the denial of the K visa petition on that basis.

Tangential point, but won't the I-129F be automatically denied because the marriage won't be legal in the Petitioner's current state? I can't imagine that's an inquiry solely for the consulate and not USCIS. 

*** Moved from K1 Progress Reports to K1 Process & Procedures ***
 
 
Your fiance should move to a state that does allow 1st cousin marriages.  Your affidavit will be next to useless to the consulate.