The short answer - you will be better off finding a human translator.
Here is a long answer. Your task has two parts.
Convert handwritten Russian into a computer text in Russian.
Translate text from Russian to English.
The second step is relatively easy. A half decent translation can be done with Google Translate.
However the first step is difficult to complete automatically. I have not heard of a web applications for OCR (optical character recognition). There are some good desktop applications such as FineReader. However, such applications are suitable for printed materials only.
There were attempts to implement OCR for handwritten texts, but they always include a training step. It's when the user "teaches" the application to recognize individual letters. To do that the user needs to understand well the handwriting and the language. After recognition is finished a user is expected to proofread the result and fix some typos. I would expect to find multiple errors after recognizing a handwritten text. Additionally, there are mistakes, colloquialisms, shortened words made by the writer.
It's nearly impossible to pre-program an application to recognize all kinds of handwriting. Handwriting changes not only from person to person, but also from generation to generation. No doubt you are comfortable with English handwriting. Please take a look at sample from 1878 and sample from 1913 Both samples are written by someone who was considered having fine writing skills in their time. Those samples may demonstrate the complexity of the task. Questions about reading records are very common in Genealogy SE.
As I understand you do not understand Russian well. Hence you won't be able to "train" the software if you find some. Then you won't be able to proofread the text before using an automated translation software. As a result you do need help from a native speaker.
You may want to consider going to a local Orthodox Church (Russian or Ukrainian) in your area, and asking for help there.