They do seem to come in all sizes.
As for Japanese influence, everything I have found in my research shows that the dha/daab form developed completely independently of the Japanese katana. The resemblance really is quite superficial, if you compare them side-by-side. The dha has a very pronounced distal taper - the katana has very very little. This gives them very different points of balance. The tang of the dha is very short (2-4 inches), trianglular, and is not pinned, nor does it even go all the way through the handle - the katana has a long, wide tang almost the length of the handle, held by pins. Dha have a more acute cross-section (don't quite know how to describe it - widest at the spine, and tapering all the way to the edge), while the katana generally has a thicker blade, with the edge taper beginning further away from the spine. Dha handles have a round cross section, katana have an oval cross section.
I say "dha," but the same applies for Thai daab. In Thailand there was some stylistic influence, but it still was fairly superficial and limited. Katana blades were popular at one point, but this was centuries after the daab form had already developed. The period of strongest Japanese influence in Thailand was in the early 17th century, and it was short-lived. The Japanesese were largely expelled from the country by the mid-16th century, with China again becoming the pre-eminant trade partner.
If there is an external influence at all, and I find that sort of condescending - as if the Tai & Burmese could not come up with their own sword designs - it would be from Yunnan (southern China today). Given that the Tai (which includes the "Shan," Lao & Thai) originally came from the Yunnan area, it still isn't really proper to call this "influence," though my current guess is that the Tai styles did influence the Burmese somewhat.
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