The following informations might be useful for transferring only the search engines and their associated keywords to another profile. I didn’t find a way to do it which would be endorsed by the developers, so following this may be risky or may not work with a different version of Firefox. Mine is iceweasel 17.0.6, it works there.
It appears from my tests that information related to the Search engines and keywords are stored in the files search.json and search-metadata.json, and in the folder searchplugins, all three in the Firefox profiles folder. Just copy from the source profile, erase on the target profile does the trick for me. Do this while Firefox is closed (and after having backed up your profile of course).
I couldn’t find much relevant official information, but here is what I found in case someone wants to investigate further or correct the doc (which I did not do because I do not know how general my conclusions based on my own tests are). This page from MozillaZine Knowledge Base (KB) says that the file search.sqlite is “no longer used in current Firefox versions”. According to my tests, this is partly incorrect: deleting the file seems to make Firefox rebuild its Search Engines list. This page from the KB also has informations which do not apply to my version. It says about the file search.json: “Not clear what it is since there is no search.sqlite to cache”, and does not mention search-metadata.json. This page from the KB, although having a promising title, does not contain much useful information. Someone did some related research, but it is probably now outdated.
My findings are based on the following tests (on a linux box). I set a keyword for one of the Search Engines, closed Firefox, and ran "grep -rl mykeyword *" in the related Firefox profile folder, which gave me only search-metadata.json. Similarly, searching for the name of one of the Search Engines ("grep -rl CNRTL *") gives only the file search.json. I also checked the content of the file "search.sqlite" (because it has a seemingly relevant name): ran "sqlite3 search.sqlite" then ".dump" to see the content of the database. It had only one table with only one entry (something about google). Also the file does not get updated when I change the search engines, whereas the other two do.