The rectangular output has even faster slopes. So the easy way would be to use separate buffers for the sine and rectangular signal. For the digital part something like 74HC04 / 74HCT14 or similar, using 4 gates in parallel could be a simple solution. 4x180 Ohm can combine the outputs and give it an approximately 50 Ohms termination and some protection.
For the sine wave there are plenty of OPs fast than the 741. It can get tricky on the prototype area to go all the way to 40 MHz as the fast OPs also need good decoupling and are often available in SMD only. An important parameter is the supply that is available. If there is a +-5 V to +-15 V supply I would consider the good old NE5534 / 5532. It should be good to some 5 MHz. One should still have termination (e.g. 50 Ohms) at the output, even if it is only to isolate the OP from the capacitance of the cable. With a 12 V supply one could use AC coupling to bring the sine signal to about the center and also have the output AC coupled. The supply splitter could be an option too to make it a +-6 V.
For the "noise" / interference, part of this could be due to the cabling. Chances are an electrolytic cap (some 100 µF) near the DDS board at the supply could help somewhat.
The offset pins at the OP are usually there to trim the OPs own offset, usually < +-5 mV. Using them to add more offset can cause problems.