A collection of historical and genalogical records
My understanding is that if there is a Douglas (maiden name) female in the line between the Douglas of 10 generations ago and the living Douglas of today, then there is no point in doing the yDNA test.
$700 sounds high to me as I think of the recent offers by Family Tree DNA.
FTDNA kit #78870
If there is no male named Douglas in your line for 10 generations, a DNA test wouldn't do anything to prove or disprove your Douglas ancestry or connect you with a particular line of Douglases. A Y-chromosome DNA test, whether it is a $120 for STR markers or a $700 test for a relatively complete look at SNPs, will only tell if your cousin may be related to others that descend from a common Male Line ancestor generations back. It is a property of the Y-chromosome that is passed from father to son virtually unchanged, generation after generation. Absent adoptions or other "non-paternal-events," these tests are basically for study of a single surname in all the generations, as presumably surnames pass from father to son virtually unchanged, generation after generation.
The family finder kind of test works on all the chromosomes and tries to match relatively close cousins independent of whether the common ancestry is all male, all female, or a mix. There wouldn't be much of a match after 10 generations. We have found a couple of third cousins (common ancestor 5 generations back) but it is real hit and miss. You can get one of those tests from 23andMe for $99.
Save the money , you will be $$$ ahead and have as many answers afterwards as you do right now .