Language contact has always existed. This also happens between sign languages and spoken languages. How do spokenl languages influence sign languages? How do sign languages influence spoken languages? Is there research on this?
Although I am not sure what are you referring to, but I might say sign language is just a natural language as all other oral language we use. There are plenty of research happening how to build efficient two-way dictionary(SL to Spoken and vice-versa) to mitigate communication gap.
Getting back to your question, lets assume you are talking about a scenario when two individuals try to communicate and one of them has SL as preference and other one prefers spoken language. If this is the scenario you referring to, there have been some research out there and most of them involves American Sign Language and English language.
The research papers are as follows:
Conference Paper Deaf and hard-of-hearing users' preferences for hearing spea...
Conference Paper Behavioral Changes in Speakers who are Automatically Caption...
Hope this helps. Feel free to checkout my research on sign language dictionary you may also find some reference there.
I was interested in language contact and how one language can influence another. For example, in the case of Libras (Brazilian Sign Language) we have many linguistic borrowings from the Portuguese language. Some signs are spelled using the sign alphabet and others use a hand configuration that refers to the initial letter of the Portuguese word. In addition, we can also observe a lot of influence on the Libras syntax. Now about the other question, could a sign language also influence an oral language, in a small community, perhaps influencing prosodic or even pragmatic aspects of the oral language?