Yeah, I know that F310 is wired. They are one family of controllers, though, so I think yours should work too (of course you can never be100% sure of anything in the wonderful land of PC).
I attached a screenshot of the dosbox mapper. You assign things with mouse - for example, to assign strafe right to the right trigger I selected "9" on the numpad , clicked on "add" and then pressed the right trigger. The screenshot shows the result.
The default controls for different systems are listed on Stella's Tomb Raider Site (
http://tombraiders.net/stella/walks/controls/TR1controls.html), I just based my configuration on Playstation layout with some modifications - namely I switched jump and action (I prefer it that way).
Oh, and the game crashes (well, it did for me) if you try to assign buttons other than XYBA in the ingame configurator (in the controls/user keys menu, not the dosbox mapper). You can assign those four ingame and they will work, or you can just assign everything in dosbox mapper and don't bother with it.
When you finish assigning, just press save and then exit. Your Tomb Raider 1 directory should now contain additional file named "mapper-SVN.map". This is the mapper file, it is possible to edit it in notepad or some other editor, if need be.