And why two directors? - Your opening a can of worms taking on someone elses risk assessments.
Why is that then?
True, if the bank demand personal guarantees, they'll check the credit ratings of the directors. However, if those two directors are linked personally, surely so are their credit histories anyway?
If the governance of the business is genuinely between the two of you, it makes sense to have two directors. However, if the two directorships are purely for the purpose of distributing the profits, there's no reason not to make one person a director, and the second person a non-director shareholder, and possibly also an employee. (Note, if the second person is a spouse, beware of a thing called S660 - lots of information online about how to comply with the current rules, but if you're both working in the business, it shouldn't be an issue).
Also, re Bazzais' suggestion of taking a personal loan as a sole trader, you can also do that as a ltd company director if you wish. Just take out a personal loan, then in turn loan that money to the limited company. You can then charge the company a commercial rate of interest on the loan, which to be beyond reproach, will be the same rate of interest that you're paying the bank.
Oh, and get a good accountant!!
HTH!