If you list the people who are still alive that could be tested and their probable relation to your great grandfather then it becomes clearer what can be achieved.
There are two main types of test to consider. YDNA tests which as you surmised must be taken by a male from the male line to be tested. Or an autosomal test which can be taken by anyone.
Note if you are going for the YDNA test then it MUST be from an unbroken male line. You indicate that your grandfather was his son and your mother was his granddaughter. Thus the YDNA chain is broken with your mother, so your brother cannot YDNA test to answer your question as they got their YDNA from your fathers side not from your mothers.
You need a brother of your mother, or a son of your mothers brother, or your grandfathers brother or a son of your grandfathers brother. Etc. It MUST be an unbroken male line otherwise you are testing the wrong branch of the family.
For YDNA you can get matches for dozens of generations back. For autosomal DNA matches you can test yourself but as Peter says the closer the person is to your great grandfather the greater the match potential.
Your problem with any test will be you won't have a sample of your great grandfathers to compare against. Since there is a second marriage involved the simplest but pricey way would be to have at least one preferably two or more people, test from each marriage.
If you are limited in the testing to only autosomal testing then you have to eliminate the chunk of DNA inherited from your great grandmother that both sides will likely have in common. If you are lucky enough to have a known male descendant in an all male line from the first marriage and from the second you will be able to compare those results with an all male line from your own family. This lucky situation is rare hence resorting to autosomal testing.