There are four translated revision lists for Nesvizh (60 km away), spanning 1834 to 1879. If revision lists exist for Nesvizh, it seems plausible that they also exist for other shtetls in the region, like Nowogrudek (Novaradok).
The Yizkor book for Nowogrudek includes about 30 perished Jews named Abramowitz. The name index is at the back of the book. The book also includes an equally long list of Abramowitz who lived in Nowogrudek and another list of Abramowitz citizens in Korelitz. The century is not entirely correct for your search, but some of these people would have been born in the 19th century.
Korelitz (Karelichy, 15 km away) had many Abramowitz. Korelitz survivor Yaakov Abramowitz's (z'l) daughter in Israel has personal records, including photographs, one of which included my great uncle. I reached Yaakov's daughter through researcher Ann Belinsky in Israel, who edited the Yizkor book for Korelitz. (The Korelitz Yizkor book does not have a list of names...the Korelitz names are listed in the Nowogrudek Yizkor book.)
Nowogrudek is known for the tunnel that Jews dug to escape the ghetto. Most of those who survived this daring escape joined the Bielski Partisans. Commemorating this, there is a Jewish Resistance Museum in Nowogrudek. The museum director is Tamara Vershitskaya. Tamara surprises me with the information that she has collected. She found the abandoned farm where my grandmother was born. Maybe Tamara has a surprise for you? If there are Abramowitz descendants from Nowogrudek, Tamara may know them.
Jack Kagan (z'l) was a survivor of Nowogrudek and he was instrumental in preserving records for Nowogrudek. This included authoring a book about Nowogrudek. I corresponded with his daughter a year or two ago. She may be another search venue for you.
If you need help contacting these people, let me know privately. I am reluctant to post personal contact information in a public forum.
Ken Domeshek - Houston
Damesek - Nesvizh
Braverman - Nesvizh
Kartorzynski - Korelitz, Nowogrudek, Negnewicze
Sinienski - Negnewicze, Wsielub, Lyubcha
Simonowitz - Negnewicze