Adding sweeteners would make sense (compare the ingredients: https://www.ussmokeless.com/-/media/Project/Altria/USSTC/products/our-products-and-ingredients/ingredients-pdfs/Copenhagen-Ingredients.pdf), but I would advise running a search for some study with smokeless tobacco analysis data, covering the range of sweetener amounts in various smokeless tobacco products. Obviously, can be added to one’s taste, but excessive (wrongly guesstimated) amounts of some sweeteners might taste off or even impair the texture.
Here’s a link to a report on menthol and methyl salicylate (wintergreen flavour) levels in some American oral tobacco products: https://www.researchgate.net/publication/40773677_Levels_of_mint_and_wintergreen_flavorants_Smokeless_tobacco_products_vs_confectionery_products.
LorAnn Wintergreen Oil and Wintergreen Flavour (both are of virtually the same strength, the former containing natural methyl salicylate, the latter - artificial) can be used (with all due caution*) to flavour smokeless tobacco products, but these flavourants cannot be added in their concentrated form and should be diluted.
Since you don’t want your dip to be any moister than it comes from the factory, consider drying it out, partially, before adding the diluted flavour. I would reduce the weight of 34 g (1.2 oz) natural dip by 5 g (down to 29 g, by drying out) and recondition it with a mixture of 0.5 g Wintergreen Flavour and 4.5 g water (and sweetener,** if you will), mixing the dip with said mixture thoroughly and letting to rest overnight before taking a wad.
Related discussion: Reddit - Dive into anything
*methyl salicylate is toxic; using a scale with 0.01 g graduation is a must.
**up to 3 mg Acesulfame K in 1 g oral tobacco
up to 70 mg xylitol in 1 g oral tobacco
up to 7 mg licorice extract in 1 g oral tobacco
P. S. Stokers Long Cut Green contains 28 mg methyl salicylate (witergreen flavouring) in 1 g product. Smoking Info