I assume it will work but the charging power will be reduced or slower than normal because the voltage input is lower in the US
I see your line of reasoning, but I'm afraid it doesn't work like that. The output from the power unit will simply not be enough to charge the battery at all. The only way it would work is if the charger is really one of the switched-mode types which will accept a wide voltage input range (e.g. 90 to 250V) but is just labeled for 230V only. That's not very likely.
Your two options would be to use a 120-to-240V step-up transformer, or to use an adapter lead to connect directly to a 240V U.S. outlet. All but the oldest of American residential house services have 240V as well as 120V, used for heavier appliances such as the range, dryer, heating, and so on.
If you can find a 240V 15A or 20A receptacle you could connect to that. Typical locations for those would be an A/C unit or some higher-powered baseboard heaters.
One other word of warning: The frequencies used by many walkie-talkies in the U.K. are different from those in use in the U.S., so you may well be in violation of F.C.C. regulations by using U.K. units Stateside.