Actually it looks like most years of the Trek 850 had Rapidfire trigger shifters. Yes you can change to trigger shifters. This one should work: Shimano Altus SL-M310 Rapid Fire Shifter - Right, 7-Speed (make sure and buy it mate too - the left one) or
SRAM X3 7 Speed Trigger Shifter Set | Chain Reaction Cycles . Be careful if you decide to go with something like this: http://www.amazon.com/Shimano-EF-51-.../dp/B00JDA3PCS because you will need to consider the type of brakes you have (long pull or short pull), but if you can determine that this one will work it may be the best option because it comes with cables, which you may or may not have to replace with the shifters above.

The ones above are "cost effective." not sure if quality shifters (more expensive) are available for 7-speed.

Also you may want to read and heed this thread if you are thinking of using 8 or 9 speed shifters:
http://www.bikeforums.net/bicycle-me...fters-mtb.html