A small digital scale could still help, if you don't mind puzzling over a little arithmetic...
It's best for eggs to lose weight steadily, which would mean losing the same percentage each week. Do a bit of research and find out what percentage turkey eggs are supposed to lose over the whole incubation. And with a calculator and a few scribbles you can figure it out from there, cause even though you don't know what the starting weight of the eggs is, you can figure out at what rate they are losing moisture, and compare that to the recommended rate, then decide if you need to lower or raise your humidity depending on if they are losing weight too slow or too fast. Get some graph paper and draw some graphs. Pictures usually make things clearer for me anyway.
Like this... A chicken egg should lose between 12% and 15% of its weight during the 18 days of incubation before you go into lockdown. So an egg that started at 100g should end up weighing 85-88g. Put that on a graph, with the weight of the egg on the up/down axis and the days on the left/right axis, and you'll get a line that slopes down the way from left (day 1) to right (day 18). You can draw two lines for the two end weights to show the acceptable upper and lower rates of moisture loss. Now if you take any 7 day period between days 1-18, you can see the ideal start and end weights, and with a quick calculation you can see what the percentage weight loss should be for any 7 day period, and check it against your own eggs.
Not as accurate as having a start weight, but still worth trying out.