There are no widespread terms in English that similarly describe an older, unmarried man in a negative way. However, you could use some less common terms with a similar meaning, such as:
* Bachelor: While this term is neutral, it can sometimes carry a connotation of being unmarried for a long time.
* Old bachelor: This term explicitly suggests an older, unmarried man.
* Confirmed bachelor: This term implies a man who has chosen to remain single.
However, it's important to remember that these terms are not typically used with the same negative connotation as "spinister." It's generally considered more respectful to avoid using negative language to describe someone based on their marital status or age.