Visiting the US after visiting Yemen [closed]

I am a British citizen with a British passport, and have travelled quite extensively for holidays. I like going off the beaten track, and am seriously contemplating a trip to the Yemeni island of Socotra. This question is not about the safety of that trip. I'm aware of the UK government's advice on visiting Yemen, but have also done considerable research into Socotra specifically, and am currently of the view that this particular trip (which would avoid mainland Yemen entirely) would be sufficiently safe. Edit: Obviously further research is needed on this point, but that's not the point of this question.

However, Socotra is in Yemen, and anyone who has visited Yemen (since 2011) is not eligible to use the Visa Waiver Program when visiting the United States. If I'm honest, the US is not my favourite country, and I'm unlikely to want to visit the country frequently or at short notice, but neither do I want to preclude returning to the US. In principle I know I can still apply for a US visa, but I'm trying to ascertain how likely it is that my application will be successful.

I've visited the US three times previously under the Visa Waiver Program, and have never had difficulty getting visas when visiting other countries. Other than liking to visit obscure holiday destinations, there's no reason why I would ever anticipate a problem getting a visa. I have no police record or history of overstaying my visa; I can easily document having the financial resources to finance any visit I'm likely to make; and I have various financial, professional and family ties to the UK. But I know that if I am declined a visa once it can make it harder to obtain future visas, including for different countries, so I'm trying to find out more about that risk before deciding whether to visit Socotra. Unfortunately the only information I have managed to locate is from those with a vested interest in persuading me to visit Socotra. Can anyone give me advice or direct me to further information?