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Replacing the sprocket on an IGH is straightforward, although things can ping off around the workshop. It can be done at home as long as you have basic tools and follow some instructions. As long as the cable outer is long enough to still reach the first cable stop on the frame and not be put under tension when the bars are turned all the way to the left and right, then changing bars is not an issue.
ffm-
Thanks so much for the reply @ffm. I've ordered a 21T sprocket to replace the 16T. I took a look at the rear dropout and don't see a whole lot more latitude for moving the wheel forward to accomodate the larger sprocket - so perhaps a new chain will be needed?
Here's a better image of the bike - https://hfc.azureedge.net/media/products/pics_and_docs/avenue/2021/901203250-1.jpg
exteroceptive
Dealing with a bike similar to this one - https://billigcykel.dk/shop/avenue-broadway-sort-6802p.html
Shimano Nexus 7 internal gear hub, and 46T front chain ring. Right now the gearing is too high for the bike's not inconsiderable weight and the lumpy terrain it's used on. What would be the best way to remedy this?
I was looking at a 38T chainring from Shimano, but it appears that maybe you can change the sprocket on the IGH instead? Would that be an easy enough job for the LBS?
I'm also thinking of changing the handlebars to something with a bit more sweep, would that affect things wrt the cable tension on the shifter?