Modifying your bike will void your warrenty.
Biggest US internet supplies I've found are modernbike.com and thebikeshopstore.com. Davidbrown in UK is highly competent but stuff might get stolen in customs like my recent Newark order.
Competitioncycling is competent but carries only high end racing gear. I bought my helmet there since only racers prevent breaking their chin with a chin guard.
No US supplier provides any dimensions on anything they sell. The tooth count might be right. Whether the mount holes will line up is totally up to chance, and your estimation of the picture. Shimano & sun websites are worthless on dimensions, pretty good on sales blather. I bought 4 rear sprockets and none of them fit.
A LBS might be able to send things back and get an actual support person on the phone. You'll pay a decent markup. Both my LBS have sold me garbage for accessories, and one dumped me on the street with improper assembly of a MBT, so I don't buy anything there but tires anymore. If you're not buying a top end racing cycle or getting it maintained don't expect much competence at a small city (2 million) LBS.
Count your teeth and estimate how much slower you want to go. You'll also need a chain splitter and master link to shorten the chain. Chains come in different widths, count the number of sprockets on the back axle to get the right one. The schwinn chain splitter doesn't work. The dodge small industrial splitter only works on single speed or 5 sprocket chain. Industrial 1/2" master links fit single speed & 5 sprocket (15 speed) chain.