I'd be inclined not to, unless you want to mix the ash with a large amount of other wood ash for example. The amount of potash you'd get is not worth it.
A lot of chlorine is used in paper manufacture, especially office paper, and when paper is burnt there will be small amounts of dioxin in the ash. While it's probably not harmful at low levels, some claim dioxins are hazardous at any level as they are carcinogens and mutagens.
You could mix it in the compost heap where it would be diluted with everything else but it would be better to send the shredded paper for recycling. After all, the shredding has already removed any security risks and even it goes to a municipal incinerator, these operate at high temperature to reduce dioxin risks.

Also the ash is extremely alkaline and potentially very toxic to many plants. You can easily compost, rather than burn the shredded paper though.