Is it possible/worth it to replace just shifters and derailleurs on an older MTB?
The great thing about bikes is that almost anything is possible for the home mechanic. But only you can answer the question of whether it's worth it. 

Deraillers almost never "wear out", at most they need new jockey wheels. They can get damaged or bent, often is is the hanger that is bent not the derailluer. 

So likely all you need is a new shifter, fortunately 7spd is a lot less complicated than bikes with more speeds. $17 for a new shifter 

http://www.jensonusa.com/!q!CCO3MwJWuenvYwhoKCsA!/Shimano-M310-Shift-Lever?utm_source=FRGL&amp;utm_medium=organic&amp;gclid=CPby-unl0sMCFRRgfgodc0YAoQ

Or you could put friction shifters on for a little more cash. 

What does get worn out is the rear cogs or cassette. You might need a cassette
and chain. That's about $50 more or less. 

You can put new canti's on there without changing the levers, if you go to V-brakes you'll need new levers. Generally getting good performance out of canti's has more to do with how well you set them up rather than the exact model you use. 

So for roughly $100-$200 in parts, you can have a functional bike again. However, if you can't do the work yourself, paying someone else to do it is a long ways towards the price of a new bike. This also assumes you already have the tools ( although these repairs don't require much in the way of specialized tools. ) 

For roughly 3x what you'd spend in parts, you can get a lightly used MTB hardtail that will be a much nicer bike. If however, you enjoy tinkering around with bikes, then you really aren't concerned about the cost of parts. 

I've fixed up a fair number of older bikes and if you don't enjoy the process and satisfaction of making something old work again, it's almost never worth the effort.