Returning correct timezone offset from join
If you are not able to modify or generate a new Timezones table without daylights, you could use more than one solution.

Using CROSS APPLY

select m.meetingid, 
       m.start, 
       m.timezone, 
       m.localstarttime, 
       t.offsetmin
from   meetingtable as m
cross apply (select top 1 offsetmin
             from timezone
             where timezone = m.timezone) t;


Using sub-query

select m.meetingid, 
       m.start, 
       m.timezone, 
       m.localstarttime, 
       (select top 1 offsetmin
        from timezone
        where timezone = m.timezone) offsetmin
from   meetingtable as m;


Using GROUP BY

select    m.meetingid, 
          m.start, 
          m.timezone, 
          m.localstarttime, 
          t.offsetmin
from      meetingtable as m
left join (select timezone,  max(offsetmin) offsetmin
           from   timezone
           group by timezone) t
on         t.timezone = m.timezone;