hiya drobess....
depends on the front end you are using.... as its a bike trike the steering geometry is still set for two wheels with a sharp rake angle (angle of forks from vertical ) for leaning into corners .....as a trike dont lean, the steering is magnified and small corrections to the direction you are traveling in turn into wobbles or shakes.....the forward position of the fork centers to the steering pin can also makes things worse..... as gloom said the expensive way is leading link forks which moves the front wheel forward altering the rake angle ( makes it bigger ) and at the same time reduces the bite of the tyre ...and shake goes away.... if you want to keep your forks as atandard another way is to have offset yokes which also pushes the front wheel forward (cheaper than leading link forks but still not cheap )....
a steering damper will only " hide " the problems and not cure it plus running the tyres soft ill only cause early tyre wear....
i work part time at my mates trike shop and this is a common problem for bike trikes and boom style trikes with motorcycle front ends ..... a lot of peaple fall into the trap of bung an axle on and bingo its a trike and thats it.... but its a lot more involved than is obvious......
right turned off my serious head
...so pm me if you need to know owt more... be glad to help out........