As long as it is not the glossy kind which has toxic heavy metals in it, it's ok to compost by adding a little bit at a time. Adding too much or adding too frequently will slow down the composing process. The ink used these days in newspaper and printers is for the most part nontoxic and should be no concern. But you don't have a compost bin so that idea won't fly for you.
As far as using shredded paper, again not the glossy type, for the fireplace, there are gizmos for sale with which you can make fire logs out of shredded paper.

Urbanite, I would say get an allotment, if you can. Mix the shredded paper with fresh stable manure. Pile up on a heap mixing in a handful of carbonate of lime or chalk. Within two months you should have a suitable compost to mulch or dig into your plot. should no plots be available perhaps you can pass it on to the local allotment society.

Do you know anyone who has a rabbit or a gerbil/hampster and maybe they could use some for bedding. (try a pet shop maybe?)

Thanks for the suggestions, unfortunately none of them are what I'm looking for.
I already have a supply of fire briquettes, Loosestrife, and 3 bags to make more. I only had one real fire this winter and that was only for 'show'. I don't need a gizmo - I use a length of drainpipe and compact the paper with a bottle.

Paper can't be used as animal bedding as it also contains shredded staples - we have people at work who keep chickens and they can't use the shreddings because of the risk of injury.

My council takes away shredded paper along with the recycling and I believe it goes to make more paper. Could you find out whether yours does this? Mine always goes on the compost heap, however - it stops it getting slimy when I am adding lots of grass cuttings etc.