I would like to know where this recommendation label is posted on my trailer as to what type of tire I must use,LT or ST, if it so critical. I can not find one.
Let me try.
Your only requirement for tire replacement from a legal perspective comes from fed regs which says in part;
571.110 under 10k quoted. Over 10k 571.120 has same requirements.
S4.2.2 Tire load limits for multipurpose passenger vehicles, trucks, buses, and trailers.
S4.2.2.1 Except as provided in S4.2.2.2, the sum of the maximum load ratings of the tires fitted to an axle shall not be less than the GAWR of the axle system as specified on the vehicle's certification label required by 49 CFR part 567."
The vehicles certification placard simply has the size axles that came OEM on the trailer. Just like your trucks drivers side door certification placard has the GAWRs listed.