Weaknesses in vanity PGP keys
This method is fine (if it does actually check for short private exponents).

Any choice of public exponent is functionally and security-wise equivalent as long as it doesn't induce a short private exponent and as long as it is co-prime to $\lambda(n)$. The latter being caught by the fact that key generation won't be able to finish and the former being caught by the PKCS#1 v2.1 induced check (which I couldn't actually find, so beware!), which should check for short private exponents.