Just a caveat upfront: delving into a tank’s MAWP history and attempting certification to a certain code can be like opening Pandora’s Box.
To be pedantic, your tank has an MAWP that isn’t going to change by radiography of the welds - your tank physically remains the same. Any certification only brings assurance that the listed MAWP is actually accurate. It sounds like the tank was never certified to API 650 - how sure are you that the current MAWP is accurate? What joint efficiency was used in the MAWP calcs?
I ask this because your rated MAWP may, or may not, be able to be increased if you perform ALL the QA API 650 requires, including a hydrostat. Using the tank dimensions, thicknesses, etc, you can use the standard joint efficiency given by the code to re-rate the tank. That rating may be higher or lower than what it currently is rated. If the MAWP calc that was originally done used a joint efficiency of 100%, then you may even see a decrease in calculated MAWP unless you do 100% radiography (I believe API 650 uses 0.9 for welds spot-checked with x-ray, but don’t quote me on that).
However, be aware that doing this QA could lead to you needing to grind out and re-weld major portions of the longitudinal welds if you find any defects. Plan for the additional time and expense.