Hi Josh,
This is going to be quite a paper, if you are covering the entirety of all the range of medieval periods and types of weaponry used by all aspects of warfare by all the tribal peoples living in the varied regions of Wales and the geopolitical situations involved
In any case, I agree, very interesting topics. For the study of the swords from earlier Middle Ages basically up to the Edwardian conquest in the 13th century, the Germanic tribes were regarded as 'saeson' (=saxons) inhabiting these regions. These tribes referred to themselves as I understand as Britons, and the regions were occupied by England for centuries, becoming part of the Kingdom in the mid 16th century. The kingdom joining England and Wales was known as the Angevin Kingdom.
I would recommend "The Sword in Anglo-Saxon England" by H.R. Davidson (1962), "The Archaeology of Weapons" E. Oakeshott, and "Weapons and Warfare in Anglo-Saxon England" (ed. Sonia Chadwick Hawkes, 1989), for the earlier centuries from post Roman Britain c.3rd century up to the 12th-13th.
After that I would rely on the "Records of the Medieval Sword" by Oakeshott along with his other works, and works by Davidson on swords of the Middle Ages. General warfare is covered in most of the works on medieval knights.
Admittedly you have a lot of work ahead of you but these references are likely the best to begin with. I believe that aside from very specifically identified weapons provenanced to certain Welsh figures or events, the weapons and warfare will generally follow the categories I have mentioned. I have not searched online for specifically attributed Welsh weapons, but there may have been articles with this theme at times.
I hope this will be of some help to get you started, and look forward to anyone else out there who might know of more specific references.
Best of luck, and very best regards,
Jim