You might be able to just get tires. Bike tire size width is just an estimate based on what RIM width the MFG of the tire feels the rim width that would be optimal for the tire design. The important size is the 20". Just because you buy a 4" wide tire doesn't mean it will be 4" wide on the rim you put it on. The wider the rim, will be the wider the tire. If your fork has just under 4" width the narrower rim you have may make for a taller and narrower 4" tire. Having said that, the rims might be too narrow. I have a 1.0 so don't have ability to measure the 2.0. It's a little difficult without calipers to measure rim and fork width but do your best to get close and post that here. Close measurements will likely be close enough to give you better guidance.