It's as simple as this:

SET @sql = 'SELECT * FROM <sometable>

WHERE dateadd(hh, @tzoffset, END_DATETIME) BETWEEN @StartDate AND @EndDate'

When you work with dynamic SQL you should use parameterised statements for many reasons, and one is exactly that it is simpler.

The way you run the query is this:

EXEC sp_executesql @sql, N'@tzoffset smallint, @StartDate datetime, @EndDate datetime',

@tzoffset, @StartDate, @EndDate

You can read more about sp_executesql in my article on dynamic SQL:

http://www.sommarskog.se/dynamic_sql.html#sp_executesql

By the way, I think a better solution is

SET @sql = 'SELECT * FROM <sometable>

WHERE END_DATETIME BETWEEN dateadd(hh, -@tzOffset, @StartDate) AND dateadd(hh, -@tzOffset, @EndDate'

While longer, the first solution runs the risk that the optimzer will not use any index on END_DATETIME.