The Colt Lightning revolvers are notoriously weak and have parts subject to breakage that simply cannot be replaced. I would be very reluctant to shoot the 1877 revolver at all.

That said, your revolver's chambers accept the .38 Special case which indicates that the chambers are bored straight through (although originally chambered for the shorter .38 Colt cartridge, which was the basis for the .38 Special case). If you are dead set on shooting the old Colt you seem to have a grip on the safest approach to doing so.

Personally, my only Colt Lightning revolver (acquired from the estate of a long-time Colt employee) lives in my safe deposit box along with its factory letter and documents from the family upon sale. I won't risk it at the range, no matter how great the temptation might get to be.

YMMV.