They should be "ok".
The velocities and hence recoil that you'll be running them at will not produce sufficient recoil to cause any problems.
Only a full powered load with a very pointed bullet, and a dose of bad karma will cause a magazine detonation. And, usually, such will just blow out the magazine forward plug......
Most of my .30/30 loads run around 1,500-2,000fps and recoil is quite mild. And, seldom do I fill the magazine.
FWIW, I just miked some Lee .311-150FNGC that I've shot thousands of, and successfully killed deer with, the meplat ran 0.195". I've run these to 2,300fps+ and no problems..... (see the killed deer above !!).
If they don't have a gascheck (you didn't state), then you should limit pressures to ~20,000psi and velocities to under 1,800fps. At this recoil level, I doubt that even a pointed FMJ could set off a round in the magazine.
One of the writers for "Handloader" magazine did a series of tests with a fixture he constructed from a magazine tube and used a variety of bullets and had to "stage" the detonation as he couldn't initiate one under "normal" conditions. Hence, tube magazines are safer than most have thought.
That still dosen't mean that they are "fool proof", given an adequately motivated fool............ But relatively safe nevertheless.