Hi David,
As Tana said just put 0 in for shipping. If you are struggling to cover the cost of shipping, I would be very sure of eliminating a shipping charge. Yes you can try it for whatever length of time you want. Just edit your listings and then edit them again when you want to change them back.
Most shops it is not a matter of price, but getting the right people looking at your items. You may want to check out some of the teams for newbies and SEO (search engine optimization) before doing things like lowering prices.
I don't have any links for those types of teams, but if you search through teams you should be able to find some.
Edit to add: Zero shipping does not always garner add on sales. I have one shop that I can capture additional add ons with zero additional shipping and another that it makes not one lick of difference with add ons whether I have 0 shipping or not. It depends on the shop and the items you sell mostly.