Thank you both. It's tempting to require a signature just to be safe but then Reg. B seems to prohibit requiring a signature even on collateral documents if it is not necessary.
§1002.7 Rules concerning extensions of credit.
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(d) Signature of spouse or other person—
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(4) Secured credit. If an applicant requests secured credit, a creditor may require the signature of the applicant's spouse or other person on any instrument necessary, or reasonably believed by the creditor to be necessary, under applicable state law to make the property being offered as security available to satisfy the debt in the event of default, for example, an instrument to create a valid lien, pass clear title, waive inchoate rights, or assign earnings.
Now I see that the Commentary virtually requires a legal opinion to back up your "reasonable belief" that the signature is necessary:
Paragraph 7(d)(4).
1. Creation of enforceable lien. Some state laws require that both spouses join in executing any instrument by which real property is encumbered. If an applicant offers such property as security for credit, a creditor may require the applicant's spouse to sign the instruments necessary to create a valid security interest in the property. The creditor may not require the spouse to sign the note evidencing the credit obligation if signing only the mortgage or other security agreement is sufficient to make the property available to satisfy the debt in the event of default. However, if under state law both spouses must sign the note to create an enforceable lien, the creditor may require the signatures.
2. Need for signature—reasonable belief. Generally, a signature to make the secured property available will only be needed on a security agreement. A creditor's reasonable belief that, to ensure access to the property, the spouse's signature is needed on an instrument that imposes personal liability should be supported by a thorough review of pertinent statutory and decisional law or an opinion of the state attorney general.