Netminder Murphy picked up an injury playing for the Belfast Giants last month but was included in the preliminary 32-man squad then the final 22-strong British team.
Murphy was given as long as possible to prove his fitness for the four-team tournament in Riga but has had to be replaced by Basingstoke Bison netminder Stevie Lyle.
Meanwhile defender Weaver has also suffered an injury and will not travel, with Nottingham Panthers team-mate Steve Lee coming into the 22-man team.
Britain warm up for the final Olympic qualifier against an Import Select side on Tuesday with their first fixture against hosts Latvia following two days later.
Only the winner of the four-team tournament will qualify for next year's Winter Olympics in Sochi and Hand has faith in Lyle and Lee to successfully fill in for Murphy and Weaver.
"We knew it was always going to be touch and go with Stephen Murphy and sadly he has not made it," said Hand.
"He is a tremendous netminder and he is really disappointed not to be going, but we have a fantastic replacement in Stevie Lyle.
"Stevie is in terrific form this season with Basingstoke and he is an experienced performer in major international tournaments.
"We have also had to make a change in defence and we will miss the talents of Jon Weaver. But going in his place is a very capable replacement in Steve Lee.
"Steve is a great talent and already has experience at this level. I always said we had a very strong squad and a very strong list of replacements.
"It speaks volumes of how good our British talent is at the moment in that we lose two players so close to the tournament, but are able to bring in two quality players to replace them."
- Sports & Recreation