To answer the question - you have to go through the same checks for a mortgage no matter the size. So you'll need to pass affordability and credit checks in the same way as someone applying for a 300k mortgage. What makes us "easier" is that it is usually easier to prove you can afford a low amount than a high amount. On your incomes, provided there are no issues in your credit history, 39k should not be a problem.
I would really encourage you to see a good independent financial advisor though. Obviously it is impossible to make accurate comment in an online forum from minimal information, but taking out a mortgage in order to simply have savings (that you have no fixed intention for) could be a long term financial mistake that will cost you money over the course of years. So many factors here including age, when you plan to retire etc. But simply put, money you hold in savings currently may struggle to generate a return equal to the cost (interest) on your mortgage. This means for the life of the mortgage you will not be making any return and may be losing money. If you have no mortgage and no savings you neither gain nor lose. However, with no mortgage you can immediately start saving the money you would use to pay the mortgage and over what would be the mortgage life time you will save more.
Hence, it is usually only worth releasing equity if you actually need the money for a specific purpose. But as I say, you need proper financial advice!