Is it safe to adapt a 10-30 outlet to accept 1-15 plugs?
No, you can't use dryer cord as a permanent wiring method to extend from an existing dryer receptacle. Here is the pertinent National Electrical Code article, attention to (1):

400.12 Uses Not Permitted.  Unless specifically permitted in 400.10, flexible cables, flexible cord sets, and power supply cords shall not be used for the following:
(1) As a substitute for the fixed wiring of a structure
(2) Where run through holes in walls, structural ceilings, suspended ceilings, dropped ceilings, or floors
(3) Where run through doorways, windows, or similar openings
(4) Where attached to building surfaces

Also, non-grounding type receptacles are only allowed to be used to replace other non-grounding type receptacles, NOT to be installed as new receptacles.

406.4(D)(2) Non–Grounding-Type Receptacles.  Where attachment to an equipment grounding conductor does not exist in the receptacle enclosure, the installation shall comply with (D)(2)(a), (D)(2)(b), or (D)(2)(c).
(a)   A non–grounding-type receptacle(s) shall be permitted to be replaced with another non–grounding-type receptacle(s).
(b)   A non–grounding-type receptacle(s) shall be permitted to be replaced with a ground-fault circuit interrupter-type of receptacle(s). These receptacles or their cover plates shall be marked “No Equipment Ground.” An equipment grounding conductor shall not be connected from the ground-fault circuit-interrupter-type receptacle to any outlet supplied from the ground-fault circuit-interrupter receptacle.
(c)   A non–grounding-type receptacle(s) shall be permitted to be replaced with a grounding-type receptacle(s) where supplied through a ground-fault circuit interrupter. Where grounding-type receptacles are supplied through the ground-fault circuit interrupter, grounding-type receptacles or their cover plates shall be marked “GFCI Protected” and “No Equipment Ground,” visible after installation. An equipment grounding conductor shall not be connected between the grounding-type receptacles.

You could arguably replace the non-grounding type dryer receptacle with a 120 volt NEMA 1-15 in that enclosure but you will have to replace the 30 amp two pole breaker with a 15 amp single pole breaker. Good luck finding a mounting strap for the receptacle though.
The safest course of action is to extend another available circuit with a ground or run a new circuit.