Your current rear derailleur has road bike design limitations: officially it will not take a sprocket larger than 27 teeth, and even if you can certainly get away with a bit more, you cannot get away with 34 teeth. So you would need an mtb derailleur. Similarly, there is also a limit to the total chain length difference, and it is 37 teeth. 22 teeth difference in the front (such as in 48-38-26) and 15 teeth in the back (such as in 12-27) is precisley within the official range. Again, you can fiddle a bit, but not enormously.
Of course, if you need lower gears, then 34 teeth and a new rear derailleur is the way to go (or an expensive IRD casette with e.g. 29 teeth that will just work with your existing rear derailleur). The question is whether you do need the lower gear. I have a lot of experience with loaded touring bikes, and there you really need the lower gears offered by mtb gearing. Heavy loads make all the difference in the world. On the other hand, for a credit card tour on a lightish road bike, you need not and cannot carry the kind of load that would require such low gearing.
You did not ask about bags, but you will need some. Your choice is either a Carradice saddle bag or a Tubus Fly rack plus I think a set of Ortlieb frontrollers used at the back. The city version is some 25% cheaper and 25% lighter. Don't fill them to capacity.
Willem