As I understand it you have a male line from your grandfather (ie grandfather, father, your brother) and you have a possible name for the great grandfather. By far the easiest would be if your brother and a direct male line descendant of the alleged great grandfather could do a Y DNA test as there would be a strong correlation if true. However this requires you to be able to persuade the descendant of the alleged great grandfather to also take the test. If this was not possible you could get your brother to take a Y DNA test with a site like
www.ftdna.com and compare it with their surname groups. However this is a bit hit and miss as
1. genealogical DNA testing is very much a minority think
2. most of the testers are actually American
3. not everyone who tests reveals their results
I would have a further look at the ftDNA website and see if there is a group for the surname you are searching and whether its worth going down this track.
Alternatively if the name is confined to a small geographical area you could put an advert in a family history magazine or the magazine of the appropriate local family history society to see if someone with a proven lineage back to the suspected person would also test
The ftdna.com website has a range of tests and prices to match worth a look, there are other testers but I have quoted this one as it is the biggest
Hopefully someone more knowledgeable in the subject will come forward and give some more suggestions